(2x)(x+39)=180

Solution for (2x)(x+39)=180 equation:

(2x)(x+39)=180

We move all terms to the left:

(2x)(x+39)-(180)=0

We multiply parentheses

2x^2+78x-180=0

a = 2; b = 78; c = -180;
Δ = b2-4ac
Δ = 782-4·2·(-180)
Δ = 7524
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:

$\sqrt{\Delta}=\sqrt{7524}=\sqrt{36*209}=\sqrt{36}*\sqrt{209}=6\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{209}}{2*2}=\frac{-78-6\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{209}}{2*2}=\frac{-78+6\sqrt{209}}{4}
$