90x-x^2-800=0

Solution for 90x-x^2-800=0 equation:

90x-x^2-800=0

We add all the numbers together, and all the variables

-1x^2+90x-800=0

a = -1; b = 90; c = -800;
Δ = b2-4ac
Δ = 902-4·(-1)·(-800)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-70}{2*-1}=\frac{-160}{-2}
=+80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+70}{2*-1}=\frac{-20}{-2}
=+10
$