180=4x(2x+6)

Solution for 180=4x(2x+6) equation:

180=4x(2x+6)

We move all terms to the left:

180-(4x(2x+6))=0


We calculate terms in parentheses: -(4x(2x+6)), so:

4x(2x+6)

We multiply parentheses

8x^2+24x

Back to the equation:

-(8x^2+24x)


We get rid of parentheses

-8x^2-24x+180=0

a = -8; b = -24; c = +180;
Δ = b2-4ac
Δ = -242-4·(-8)·180
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{11}}{2*-8}=\frac{24-24\sqrt{11}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{11}}{2*-8}=\frac{24+24\sqrt{11}}{-16}
$