(x+6)(5x-6)=108

Solution for (x+6)(5x-6)=108 equation:

(x+6)(5x-6)=108

We move all terms to the left:

(x+6)(5x-6)-(108)=0

We multiply parentheses ..

(+5x^2-6x+30x-36)-108=0

We get rid of parentheses

5x^2-6x+30x-36-108=0

We add all the numbers together, and all the variables

5x^2+24x-144=0

a = 5; b = 24; c = -144;
Δ = b2-4ac
Δ = 242-4·5·(-144)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{6}}{2*5}=\frac{-24-24\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{6}}{2*5}=\frac{-24+24\sqrt{6}}{10}
$