100+90x-x^2=0

Solution for 100+90x-x^2=0 equation:

100+90x-x^2=0

We add all the numbers together, and all the variables

-1x^2+90x+100=0

a = -1; b = 90; c = +100;
Δ = b2-4ac
Δ = 902-4·(-1)·100
Δ = 8500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8500}=\sqrt{100*85}=\sqrt{100}*\sqrt{85}=10\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-10\sqrt{85}}{2*-1}=\frac{-90-10\sqrt{85}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+10\sqrt{85}}{2*-1}=\frac{-90+10\sqrt{85}}{-2}
$