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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+36x^2-24x-120x+80)), so:

(+36x^2-24x-120x+80)

We get rid of parentheses

36x^2-24x-120x+80

We add all the numbers together, and all the variables

36x^2-144x+80

Back to the equation:

-(36x^2-144x+80)


We get rid of parentheses

-36x^2+144x-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}
$