(6x-4)(6x-20)=180

Solution for (6x-4)(6x-20)=180 equation:

(6x-4)(6x-20)=180

We move all terms to the left:

(6x-4)(6x-20)-(180)=0

We multiply parentheses ..

(+36x^2-120x-24x+80)-180=0

We get rid of parentheses

36x^2-120x-24x+80-180=0

We add all the numbers together, and all the variables

36x^2-144x-100=0

a = 36; b = -144; c = -100;
Δ = b2-4ac
Δ = -1442-4·36·(-100)
Δ = 35136
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:

$\sqrt{\Delta}=\sqrt{35136}=\sqrt{576*61}=\sqrt{576}*\sqrt{61}=24\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-24\sqrt{61}}{2*36}=\frac{144-24\sqrt{61}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+24\sqrt{61}}{2*36}=\frac{144+24\sqrt{61}}{72}
$