H=5+70t-16t^2

Solution for H=5+70t-16t^2 equation:

=5+70H-16H^2

We move all terms to the left:

-(5+70H-16H^2)=0

We get rid of parentheses

16H^2-70H-5=0

a = 16; b = -70; c = -5;
Δ = b2-4ac
Δ = -702-4·16·(-5)
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-6\sqrt{145}}{2*16}=\frac{70-6\sqrt{145}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+6\sqrt{145}}{2*16}=\frac{70+6\sqrt{145}}{32}
$