H=2+70t-16t^2

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

=2+70H-16H^2

We move all terms to the left:

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

We get rid of parentheses

16H^2-70H-2=0

a = 16; b = -70; c = -2;
Δ = b2-4ac
Δ = -702-4·16·(-2)
Δ = 5028
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:

$\sqrt{\Delta}=\sqrt{5028}=\sqrt{4*1257}=\sqrt{4}*\sqrt{1257}=2\sqrt{1257}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1257}}{2*16}=\frac{70-2\sqrt{1257}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1257}}{2*16}=\frac{70+2\sqrt{1257}}{32}
$