180=2x(2x+3)

Solution for 180=2x(2x+3) equation:

180=2x(2x+3)

We move all terms to the left:

180-(2x(2x+3))=0


We calculate terms in parentheses: -(2x(2x+3)), so:

2x(2x+3)

We multiply parentheses

4x^2+6x

Back to the equation:

-(4x^2+6x)


We get rid of parentheses

-4x^2-6x+180=0

a = -4; b = -6; c = +180;
Δ = b2-4ac
Δ = -62-4·(-4)·180
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-54}{2*-4}=\frac{-48}{-8}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+54}{2*-4}=\frac{60}{-8}
=-7+1/2
$