1500=200x-5x^2

Solution for 1500=200x-5x^2 equation:

1500=200x-5x^2

We move all terms to the left:

1500-(200x-5x^2)=0

We get rid of parentheses

5x^2-200x+1500=0

a = 5; b = -200; c = +1500;
Δ = b2-4ac
Δ = -2002-4·5·1500
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-100}{2*5}=\frac{100}{10}
=10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+100}{2*5}=\frac{300}{10}
=30
$