180=6x(x+20)

Solution for 180=6x(x+20) equation:

180=6x(x+20)

We move all terms to the left:

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


We calculate terms in parentheses: -(6x(x+20)), so:

6x(x+20)

We multiply parentheses

6x^2+120x

Back to the equation:

-(6x^2+120x)


We get rid of parentheses

-6x^2-120x+180=0

a = -6; b = -120; c = +180;
Δ = b2-4ac
Δ = -1202-4·(-6)·180
Δ = 18720
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:

$\sqrt{\Delta}=\sqrt{18720}=\sqrt{144*130}=\sqrt{144}*\sqrt{130}=12\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-12\sqrt{130}}{2*-6}=\frac{120-12\sqrt{130}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+12\sqrt{130}}{2*-6}=\frac{120+12\sqrt{130}}{-12}
$