2x(x+72)=180

Solution for 2x(x+72)=180 equation:

2x(x+72)=180

We move all terms to the left:

2x(x+72)-(180)=0

We multiply parentheses

2x^2+144x-180=0

a = 2; b = 144; c = -180;
Δ = b2-4ac
Δ = 1442-4·2·(-180)
Δ = 22176
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:

$\sqrt{\Delta}=\sqrt{22176}=\sqrt{144*154}=\sqrt{144}*\sqrt{154}=12\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-12\sqrt{154}}{2*2}=\frac{-144-12\sqrt{154}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+12\sqrt{154}}{2*2}=\frac{-144+12\sqrt{154}}{4}
$