x(4x-2)=90

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

x(4x-2)=90

We move all terms to the left:

x(4x-2)-(90)=0

We multiply parentheses

4x^2-2x-90=0

a = 4; b = -2; c = -90;
Δ = b2-4ac
Δ = -22-4·4·(-90)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*4}=\frac{40}{8}
=5
$