(5x-13)(2x-16)=90

Solution for (5x-13)(2x-16)=90 equation:

(5x-13)(2x-16)=90

We move all terms to the left:

(5x-13)(2x-16)-(90)=0

We multiply parentheses ..

(+10x^2-80x-26x+208)-90=0

We get rid of parentheses

10x^2-80x-26x+208-90=0

We add all the numbers together, and all the variables

10x^2-106x+118=0

a = 10; b = -106; c = +118;
Δ = b2-4ac
Δ = -1062-4·10·118
Δ = 6516
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:

$\sqrt{\Delta}=\sqrt{6516}=\sqrt{36*181}=\sqrt{36}*\sqrt{181}=6\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-6\sqrt{181}}{2*10}=\frac{106-6\sqrt{181}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+6\sqrt{181}}{2*10}=\frac{106+6\sqrt{181}}{20}
$