(6x-6)(x+2)=76

Solution for (6x-6)(x+2)=76 equation:

(6x-6)(x+2)=76

We move all terms to the left:

(6x-6)(x+2)-(76)=0

We multiply parentheses ..

(+6x^2+12x-6x-12)-76=0

We get rid of parentheses

6x^2+12x-6x-12-76=0

We add all the numbers together, and all the variables

6x^2+6x-88=0

a = 6; b = 6; c = -88;
Δ = b2-4ac
Δ = 62-4·6·(-88)
Δ = 2148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2148}=\sqrt{4*537}=\sqrt{4}*\sqrt{537}=2\sqrt{537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{537}}{2*6}=\frac{-6-2\sqrt{537}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{537}}{2*6}=\frac{-6+2\sqrt{537}}{12}
$