(x-13)(2x)=90

Solution for (x-13)(2x)=90 equation:

(x-13)(2x)=90

We move all terms to the left:

(x-13)(2x)-(90)=0

We multiply parentheses

2x^2-26x-90=0

a = 2; b = -26; c = -90;
Δ = b2-4ac
Δ = -262-4·2·(-90)
Δ = 1396
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:

$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{349}}{2*2}=\frac{26-2\sqrt{349}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{349}}{2*2}=\frac{26+2\sqrt{349}}{4}
$