H=5t^2-65t+25

Solution for H=5t^2-65t+25 equation:

=5H^2-65H+25

We move all terms to the left:

-(5H^2-65H+25)=0

We get rid of parentheses

-5H^2+65H-25=0

a = -5; b = 65; c = -25;
Δ = b2-4ac
Δ = 652-4·(-5)·(-25)
Δ = 3725
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3725}=\sqrt{25*149}=\sqrt{25}*\sqrt{149}=5\sqrt{149}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{149}}{2*-5}=\frac{-65-5\sqrt{149}}{-10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{149}}{2*-5}=\frac{-65+5\sqrt{149}}{-10}
$