H=-3t^2+24t-25

Solution for H=-3t^2+24t-25 equation:

=-3H^2+24H-25

We move all terms to the left:

-(-3H^2+24H-25)=0

We get rid of parentheses

3H^2-24H+25=0

a = 3; b = -24; c = +25;
Δ = b2-4ac
Δ = -242-4·3·25
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{69}}{2*3}=\frac{24-2\sqrt{69}}{6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{69}}{2*3}=\frac{24+2\sqrt{69}}{6}
$