-90x^2+8100x=x

Solution for -90x^2+8100x=x equation:

-90x^2+8100x=x

We move all terms to the left:

-90x^2+8100x-(x)=0

We add all the numbers together, and all the variables

-90x^2+8099x=0

a = -90; b = 8099; c = 0;
Δ = b2-4ac
Δ = 80992-4·(-90)·0
Δ = 65593801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65593801}=8099$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8099)-8099}{2*-90}=\frac{-16198}{-180}
=89+89/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8099)+8099}{2*-90}=\frac{0}{-180}
=0
$