Equation Calculator

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**Equation Calculator** (or) **solution set calculator**** **will help us to simplify the equations (Linear, Quadratic, Cubic, Biquadratic, etc) with respect to its given variable. It is a** ****Equation Solver** **with steps ** that calculates the roots of the given equation and plots the value on graph. Try our rearranging equations calculator (**variable Calculator**) and get your problems solved instantly.

You can see a default equation with respect to its variable given below. When u click on "Calculate", first the calculator calculates the discriminant and then find the roots of the equation by applying the appropriate formula given in the steps below.

**Step 1 :**

**Step 2 :**

**Step 3 :**

You can see a default equation with respect to its variable given below. When u click on "Calculate", first the calculator calculates the discriminant and then find the roots of the equation by applying the appropriate formula given in the steps below.

Observe the given equation.

Find the value of discriminant(D) by applying the formula D = b^{2} - 4ac.

If the value of discriminant(D) is less than zero, write "roots does not exist (or) imaginary. And if discriminant is greater or equal to zero, then find the roots of an equation by applying the formula x_{1}= $\frac{-b + \sqrt{D}}{2a}$ and x_{2} = $\frac{-b - \sqrt{D}}{2a}$

Calculate the roots of the equation: x

^{2}+ 6x + 8 = 0?**Step 1 :**Given equation: x

^{2}+ 6x + 8 = 0

So, a = 1, b = 6 and c =8

**Step 2 :**Discriminant(D) = b

^{2}- 4ac

= (6)

^{2}- 4(1)(8)

= 36 - 32

= 4

**Step 3 :**x

_{1}= $\frac{-b + \sqrt{D}}{2a}$

x

_{1}= $\frac{-6 + \sqrt{4}}{2(1)}$

x

_{1}= $\frac{-6 + 2}{2}$

x

_{1}= $\frac{-4}{2}$

x

_{1}= -2

and x

_{2}= $\frac{-b - \sqrt{D}}{2a}$

and x

_{2}= $\frac{-6 - \sqrt{4}}{2(1)}$

and x

_{2}= $\frac{-6 - 2}{2}$

and x

_{2}= $\frac{- 8}{2}$

and x

_{2}= -4**Answer :**x

_{1}= -2 and x_{2}= -4Calculate the roots of the equation: x

^{2 }+ 9x + 8?**Step 1 :**Given equation: x

^{2 }+ 9x + 8 = 0

So, a = 1, b = 9 and c =8

**Step 2 :**Discriminant(D) = b

^{2}- 4ac

= (9)

^{2}- 4(1)(8)

= 81 - 32

= 49

**Step 3 :**x

_{1}= $\frac{-b + \sqrt{D}}{2a}$

x

_{1}= $\frac{-9 + \sqrt{49}}{2(1)}$

x

_{1}= $\frac{-9 + 7}{2}$

x

_{1}= $\frac{-2}{2}$

x

_{1}= -1

and x

_{2}= $\frac{-b - \sqrt{D}}{2a}$

and x

_{2}= $\frac{-9 - \sqrt{49}}{2(1)}$

and x

_{2}= $\frac{-9 - 7}{2}$

and x

_{2}= $\frac{-16}{2}$

and x

_{2}= -8

**Answer :**x

_{1}= -1 and x_{2}= -8A company started manufacturing credit cards of area 35 cm$^2$. The length of a credit card is 2 cm more than its width. What are the dimensions of a credit card.

**Step 1 :**Let x represent the width of a credit card. Then (x + 2) represents the length of a credit card.

**Step 2 :**The shape of credit card looks like a rectangle.

According to the given statement:

x(x + 2) = 35 (Area of rectangle = Length * Width)

x$^2$ + 2x = 35

or x$^2$ + 2x - 35 = 0 ...(1)

**Step 3 :**Compare above equation with standard quadratic equation, ax$^2$ + bx + c = 0

we have, a = 1, b = 2 and c = -35

Using quadratic equation formula, i.e.

x = $\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

x = $\frac{-2 \pm \sqrt{2^2-4.1.-35}}{2}$

x = $\frac{-2 \pm 12}{2}$

x = -1 + 6 = 5 or x = -1 - 6 = -7

or x = 5 or x = -7

Width of credit cards cannot be negative, so we discard the value of x = -7.**Answer :**Width of a credit card is 5 cm and length (x + 2) is 7cm.

Jasica had taken a bank loan to buy a land. After 6 months, she sold that land for 15000 dollars and closed her loan. While selling the land, she had offered a discount of 10 % on the selling price and she earned a profit of 8 %. What is the cost price of the land?

**Step 1 :**Let the cost price of land is x dollars.

**Step 2 :**As she offered a discount of 10 % and earned 8 % profit, our equation will be

90 % of 15000 = 108 % of x**Step 3 :**$\frac{90}{100}$ $\times$ 15000 = $\frac{108}{100}$ $\times$ x

90 $\times$ 150 = $\frac{108 x}{100}$

Or 1350000 = 108x

Or x = $\frac{1350000}{108}$

Or x = 12500**Answer :**The cost price of that land is 12500 dollars.