(13x)(16x-12)=180

Solution for (13x)(16x-12)=180 equation:

(13x)(16x-12)=180

We move all terms to the left:

(13x)(16x-12)-(180)=0

We multiply parentheses

208x^2-156x-180=0

a = 208; b = -156; c = -180;
Δ = b2-4ac
Δ = -1562-4·208·(-180)
Δ = 174096
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:

$\sqrt{\Delta}=\sqrt{174096}=\sqrt{144*1209}=\sqrt{144}*\sqrt{1209}=12\sqrt{1209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-12\sqrt{1209}}{2*208}=\frac{156-12\sqrt{1209}}{416}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+12\sqrt{1209}}{2*208}=\frac{156+12\sqrt{1209}}{416}
$