H=6+75t-16t2

Solution for H=6+75t-16t2 equation:

=6+75H-16H^2

We move all terms to the left:

-(6+75H-16H^2)=0

We get rid of parentheses

16H^2-75H-6=0

a = 16; b = -75; c = -6;
Δ = b2-4ac
Δ = -752-4·16·(-6)
Δ = 6009
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{6009}}{2*16}=\frac{75-\sqrt{6009}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{6009}}{2*16}=\frac{75+\sqrt{6009}}{32}
$