H(6)=-60t^2+90t

Solution for H(6)=-60t^2+90t equation:

(6)=-60H^2+90H

We move all terms to the left:

(6)-(-60H^2+90H)=0

We get rid of parentheses

60H^2-90H+6=0

a = 60; b = -90; c = +6;
Δ = b2-4ac
Δ = -902-4·60·6
Δ = 6660
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:

$\sqrt{\Delta}=\sqrt{6660}=\sqrt{36*185}=\sqrt{36}*\sqrt{185}=6\sqrt{185}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{185}}{2*60}=\frac{90-6\sqrt{185}}{120}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{185}}{2*60}=\frac{90+6\sqrt{185}}{120}
$