(x+80)(6x)=180

Solution for (x+80)(6x)=180 equation:

(x+80)(6x)=180

We move all terms to the left:

(x+80)(6x)-(180)=0

We multiply parentheses

6x^2+480x-180=0

a = 6; b = 480; c = -180;
Δ = b2-4ac
Δ = 4802-4·6·(-180)
Δ = 234720
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:

$\sqrt{\Delta}=\sqrt{234720}=\sqrt{144*1630}=\sqrt{144}*\sqrt{1630}=12\sqrt{1630}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-12\sqrt{1630}}{2*6}=\frac{-480-12\sqrt{1630}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+12\sqrt{1630}}{2*6}=\frac{-480+12\sqrt{1630}}{12}
$