(13x)(16x-12)=90

Solution for (13x)(16x-12)=90 equation:

(13x)(16x-12)=90

We move all terms to the left:

(13x)(16x-12)-(90)=0

We multiply parentheses

208x^2-156x-90=0

a = 208; b = -156; c = -90;
Δ = b2-4ac
Δ = -1562-4·208·(-90)
Δ = 99216
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:

$\sqrt{\Delta}=\sqrt{99216}=\sqrt{144*689}=\sqrt{144}*\sqrt{689}=12\sqrt{689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-12\sqrt{689}}{2*208}=\frac{156-12\sqrt{689}}{416}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+12\sqrt{689}}{2*208}=\frac{156+12\sqrt{689}}{416}
$