180=6x(x-2)

Solution for 180=6x(x-2) equation:

180=6x(x-2)

We move all terms to the left:

180-(6x(x-2))=0


We calculate terms in parentheses: -(6x(x-2)), so:

6x(x-2)

We multiply parentheses

6x^2-12x

Back to the equation:

-(6x^2-12x)


We get rid of parentheses

-6x^2+12x+180=0

a = -6; b = 12; c = +180;
Δ = b2-4ac
Δ = 122-4·(-6)·180
Δ = 4464
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:

$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{31}}{2*-6}=\frac{-12-12\sqrt{31}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{31}}{2*-6}=\frac{-12+12\sqrt{31}}{-12}
$