4x(4x+10)=90

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

4x(4x+10)=90

We move all terms to the left:

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

We multiply parentheses

16x^2+40x-90=0

a = 16; b = 40; c = -90;
Δ = b2-4ac
Δ = 402-4·16·(-90)
Δ = 7360
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:

$\sqrt{\Delta}=\sqrt{7360}=\sqrt{64*115}=\sqrt{64}*\sqrt{115}=8\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{115}}{2*16}=\frac{-40-8\sqrt{115}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{115}}{2*16}=\frac{-40+8\sqrt{115}}{32}
$