8x(4x+5)=90

Solution for 8x(4x+5)=90 equation:

8x(4x+5)=90

We move all terms to the left:

8x(4x+5)-(90)=0

We multiply parentheses

32x^2+40x-90=0

a = 32; b = 40; c = -90;
Δ = b2-4ac
Δ = 402-4·32·(-90)
Δ = 13120
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:

$\sqrt{\Delta}=\sqrt{13120}=\sqrt{64*205}=\sqrt{64}*\sqrt{205}=8\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{205}}{2*32}=\frac{-40-8\sqrt{205}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{205}}{2*32}=\frac{-40+8\sqrt{205}}{64}
$