x=90x-2x^2

Solution for x=90x-2x^2 equation:

x=90x-2x^2

We move all terms to the left:

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

We get rid of parentheses

2x^2-90x+x=0

We add all the numbers together, and all the variables

2x^2-89x=0

a = 2; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·2·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*2}=\frac{178}{4}
=44+1/2
$