(x+30)(2x)=180

Solution for (x+30)(2x)=180 equation:

(x+30)(2x)=180

We move all terms to the left:

(x+30)(2x)-(180)=0

We multiply parentheses

2x^2+60x-180=0

a = 2; b = 60; c = -180;
Δ = b2-4ac
Δ = 602-4·2·(-180)
Δ = 5040
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:

$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{35}}{2*2}=\frac{-60-12\sqrt{35}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{35}}{2*2}=\frac{-60+12\sqrt{35}}{4}
$