-5p^2+200p=500

Solution for -5p^2+200p=500 equation:

-5p^2+200p=500

We move all terms to the left:

-5p^2+200p-(500)=0

a = -5; b = 200; c = -500;
Δ = b2-4ac
Δ = 2002-4·(-5)·(-500)
Δ = 30000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-100\sqrt{3}}{2*-5}=\frac{-200-100\sqrt{3}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+100\sqrt{3}}{2*-5}=\frac{-200+100\sqrt{3}}{-10}
$