H=5t^2-60t+30

Solution for H=5t^2-60t+30 equation:

=5H^2-60H+30

We move all terms to the left:

-(5H^2-60H+30)=0

We get rid of parentheses

-5H^2+60H-30=0

a = -5; b = 60; c = -30;
Δ = b2-4ac
Δ = 602-4·(-5)·(-30)
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-10\sqrt{30}}{2*-5}=\frac{-60-10\sqrt{30}}{-10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+10\sqrt{30}}{2*-5}=\frac{-60+10\sqrt{30}}{-10}
$