(2x-10)(4x+16)=90

Solution for (2x-10)(4x+16)=90 equation:

(2x-10)(4x+16)=90

We move all terms to the left:

(2x-10)(4x+16)-(90)=0

We multiply parentheses ..

(+8x^2+32x-40x-160)-90=0

We get rid of parentheses

8x^2+32x-40x-160-90=0

We add all the numbers together, and all the variables

8x^2-8x-250=0

a = 8; b = -8; c = -250;
Δ = b2-4ac
Δ = -82-4·8·(-250)
Δ = 8064
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:

$\sqrt{\Delta}=\sqrt{8064}=\sqrt{576*14}=\sqrt{576}*\sqrt{14}=24\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24\sqrt{14}}{2*8}=\frac{8-24\sqrt{14}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24\sqrt{14}}{2*8}=\frac{8+24\sqrt{14}}{16}
$