200x-100x^2=75

Solution for 200x-100x^2=75 equation:

200x-100x^2=75

We move all terms to the left:

200x-100x^2-(75)=0

a = -100; b = 200; c = -75;
Δ = b2-4ac
Δ = 2002-4·(-100)·(-75)
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*-100}=\frac{-300}{-200}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+100}{2*-100}=\frac{-100}{-200}
=1/2
$