90x-5x^2=200

Solution for 90x-5x^2=200 equation:

90x-5x^2=200

We move all terms to the left:

90x-5x^2-(200)=0

a = -5; b = 90; c = -200;
Δ = b2-4ac
Δ = 902-4·(-5)·(-200)
Δ = 4100
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:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-10\sqrt{41}}{2*-5}=\frac{-90-10\sqrt{41}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+10\sqrt{41}}{2*-5}=\frac{-90+10\sqrt{41}}{-10}
$