100x-25x^2=75

Solution for 100x-25x^2=75 equation:

100x-25x^2=75

We move all terms to the left:

100x-25x^2-(75)=0

a = -25; b = 100; c = -75;
Δ = b2-4ac
Δ = 1002-4·(-25)·(-75)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-50}{2*-25}=\frac{-150}{-50}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+50}{2*-25}=\frac{-50}{-50}
=1
$