(4x^2-4x-168)/(2x+12)=20

Solution for (4x^2-4x-168)/(2x+12)=20 equation:

(4x^2-4x-168)/(2x+12)=20

We move all terms to the left:

(4x^2-4x-168)/(2x+12)-(20)=0


Domain of the equation: (2x+12)!=0

We move all terms containing x to the left, all other terms to the right

2x!=-12

x!=-12/2

x!=-6

x∈R


We multiply all the terms by the denominator


(4x^2-4x-168)-20*(2x+12)=0

We multiply parentheses

(4x^2-4x-168)-40x-240=0

We get rid of parentheses

4x^2-4x-40x-168-240=0

We add all the numbers together, and all the variables

4x^2-44x-408=0

a = 4; b = -44; c = -408;
Δ = b2-4ac
Δ = -442-4·4·(-408)
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-92}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+92}{2*4}=\frac{136}{8}
=17
$