4x(5x-9)=90

Solution for 4x(5x-9)=90 equation:

4x(5x-9)=90

We move all terms to the left:

4x(5x-9)-(90)=0

We multiply parentheses

20x^2-36x-90=0

a = 20; b = -36; c = -90;
Δ = b2-4ac
Δ = -362-4·20·(-90)
Δ = 8496
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:

$\sqrt{\Delta}=\sqrt{8496}=\sqrt{144*59}=\sqrt{144}*\sqrt{59}=12\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{59}}{2*20}=\frac{36-12\sqrt{59}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{59}}{2*20}=\frac{36+12\sqrt{59}}{40}
$