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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

16x(2x+13)-86=0

We multiply parentheses

32x^2+208x-86=0

a = 32; b = 208; c = -86;
Δ = b2-4ac
Δ = 2082-4·32·(-86)
Δ = 54272
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:

$\sqrt{\Delta}=\sqrt{54272}=\sqrt{1024*53}=\sqrt{1024}*\sqrt{53}=32\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-32\sqrt{53}}{2*32}=\frac{-208-32\sqrt{53}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+32\sqrt{53}}{2*32}=\frac{-208+32\sqrt{53}}{64}
$