100=-5x^2+10x+175

Solution for 100=-5x^2+10x+175 equation:

100=-5x^2+10x+175

We move all terms to the left:

100-(-5x^2+10x+175)=0

We get rid of parentheses

5x^2-10x-175+100=0

We add all the numbers together, and all the variables

5x^2-10x-75=0

a = 5; b = -10; c = -75;
Δ = b2-4ac
Δ = -102-4·5·(-75)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-40}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+40}{2*5}=\frac{50}{10}
=5
$