H=-16t^2-145t+125

Solution for H=-16t^2-145t+125 equation:

=-16H^2-145H+125

We move all terms to the left:

-(-16H^2-145H+125)=0

We get rid of parentheses

16H^2+145H-125=0

a = 16; b = 145; c = -125;
Δ = b2-4ac
Δ = 1452-4·16·(-125)
Δ = 29025
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:

$\sqrt{\Delta}=\sqrt{29025}=\sqrt{225*129}=\sqrt{225}*\sqrt{129}=15\sqrt{129}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(145)-15\sqrt{129}}{2*16}=\frac{-145-15\sqrt{129}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(145)+15\sqrt{129}}{2*16}=\frac{-145+15\sqrt{129}}{32}
$