(16x-4)(2x+13)=90

Solution for (16x-4)(2x+13)=90 equation:

(16x-4)(2x+13)=90

We move all terms to the left:

(16x-4)(2x+13)-(90)=0

We multiply parentheses ..

(+32x^2+208x-8x-52)-90=0

We get rid of parentheses

32x^2+208x-8x-52-90=0

We add all the numbers together, and all the variables

32x^2+200x-142=0

a = 32; b = 200; c = -142;
Δ = b2-4ac
Δ = 2002-4·32·(-142)
Δ = 58176
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:

$\sqrt{\Delta}=\sqrt{58176}=\sqrt{576*101}=\sqrt{576}*\sqrt{101}=24\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-24\sqrt{101}}{2*32}=\frac{-200-24\sqrt{101}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+24\sqrt{101}}{2*32}=\frac{-200+24\sqrt{101}}{64}
$