(x-2)(x-3)=8x+8

Solution for (x-2)(x-3)=8x+8 equation:

(x-2)(x-3)=8x+8

We move all terms to the left:

(x-2)(x-3)-(8x+8)=0

We get rid of parentheses

(x-2)(x-3)-8x-8=0

We multiply parentheses ..

(+x^2-3x-2x+6)-8x-8=0

We get rid of parentheses

x^2-3x-2x-8x+6-8=0

We add all the numbers together, and all the variables

x^2-13x-2=0

a = 1; b = -13; c = -2;
Δ = b2-4ac
Δ = -132-4·1·(-2)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{177}}{2*1}=\frac{13-\sqrt{177}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{177}}{2*1}=\frac{13+\sqrt{177}}{2}
$