-x2+90x-2000=0

Solution for -x2+90x-2000=0 equation:

-x2+90x-2000=0

We add all the numbers together, and all the variables

-1x^2+90x-2000=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{-100}{-2}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+10}{2*-1}=\frac{-80}{-2}
=+40
$