2(x-6)(2x+5)=8

Solution for 2(x-6)(2x+5)=8 equation:

2(x-6)(2x+5)=8

We move all terms to the left:

2(x-6)(2x+5)-(8)=0

We multiply parentheses ..

2(+2x^2+5x-12x-30)-8=0

We multiply parentheses

4x^2+10x-24x-60-8=0

We add all the numbers together, and all the variables

4x^2-14x-68=0

a = 4; b = -14; c = -68;
Δ = b2-4ac
Δ = -142-4·4·(-68)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{321}}{2*4}=\frac{14-2\sqrt{321}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{321}}{2*4}=\frac{14+2\sqrt{321}}{8}
$