H=-5t^2+10t+175

Solution for H=-5t^2+10t+175 equation:

=-5H^2+10H+175

We move all terms to the left:

-(-5H^2+10H+175)=0

We get rid of parentheses

5H^2-10H-175=0

a = 5; b = -10; c = -175;
Δ = b2-4ac
Δ = -102-4·5·(-175)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-60}{2*5}=\frac{-50}{10}
=-5
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+60}{2*5}=\frac{70}{10}
=7
$