H=22t+15-16t^2

Solution for H=22t+15-16t^2 equation:

=22H+15-16H^2

We move all terms to the left:

-(22H+15-16H^2)=0

We get rid of parentheses

16H^2-22H-15=0

a = 16; b = -22; c = -15;
Δ = b2-4ac
Δ = -222-4·16·(-15)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-38}{2*16}=\frac{-16}{32}
=-1/2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+38}{2*16}=\frac{60}{32}
=1+7/8
$