H=-16t2+75t+4

Solution for H=-16t2+75t+4 equation:

=-16H^2+75H+4

We move all terms to the left:

-(-16H^2+75H+4)=0

We get rid of parentheses

16H^2-75H-4=0

a = 16; b = -75; c = -4;
Δ = b2-4ac
Δ = -752-4·16·(-4)
Δ = 5881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{5881}}{2*16}=\frac{75-\sqrt{5881}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5881}}{2*16}=\frac{75+\sqrt{5881}}{32}
$