2000+x^2=90x

Solution for 2000+x^2=90x equation:

2000+x^2=90x

We move all terms to the left:

2000+x^2-(90x)=0

a = 1; b = -90; c = +2000;
Δ = b2-4ac
Δ = -902-4·1·2000
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10}{2*1}=\frac{80}{2}
=40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10}{2*1}=\frac{100}{2}
=50
$