(4x)(x-5)=90

Solution for (4x)(x-5)=90 equation:

(4x)(x-5)=90

We move all terms to the left:

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

We multiply parentheses

4x^2-20x-90=0

a = 4; b = -20; c = -90;
Δ = b2-4ac
Δ = -202-4·4·(-90)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{115}}{2*4}=\frac{20-4\sqrt{115}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{115}}{2*4}=\frac{20+4\sqrt{115}}{8}
$