H=5+31t-16t2

Solution for H=5+31t-16t2 equation:

=5+31H-16H^2

We move all terms to the left:

-(5+31H-16H^2)=0

We get rid of parentheses

16H^2-31H-5=0

a = 16; b = -31; c = -5;
Δ = b2-4ac
Δ = -312-4·16·(-5)
Δ = 1281
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{-(-31)-\sqrt{1281}}{2*16}=\frac{31-\sqrt{1281}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1281}}{2*16}=\frac{31+\sqrt{1281}}{32}
$