(2x-6)(x+2)=112

Solution for (2x-6)(x+2)=112 equation:

(2x-6)(x+2)=112

We move all terms to the left:

(2x-6)(x+2)-(112)=0

We multiply parentheses ..

(+2x^2+4x-6x-12)-112=0

We get rid of parentheses

2x^2+4x-6x-12-112=0

We add all the numbers together, and all the variables

2x^2-2x-124=0

a = 2; b = -2; c = -124;
Δ = b2-4ac
Δ = -22-4·2·(-124)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{249}}{2*2}=\frac{2-2\sqrt{249}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{249}}{2*2}=\frac{2+2\sqrt{249}}{4}
$