(x+15)(2x)=180

Solution for (x+15)(2x)=180 equation:

(x+15)(2x)=180

We move all terms to the left:

(x+15)(2x)-(180)=0

We multiply parentheses

2x^2+30x-180=0

a = 2; b = 30; c = -180;
Δ = b2-4ac
Δ = 302-4·2·(-180)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{65}}{2*2}=\frac{-30-6\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{65}}{2*2}=\frac{-30+6\sqrt{65}}{4}
$