H=2+90t+-16t2

Solution for H=2+90t+-16t2 equation:

=2+90H+-16H^2

We move all terms to the left:

-(2+90H+-16H^2)=0

We use the square of the difference formula

-(2+90H-16H^2)=0

We get rid of parentheses

16H^2-90H-2=0

a = 16; b = -90; c = -2;
Δ = b2-4ac
Δ = -902-4·16·(-2)
Δ = 8228
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:

$\sqrt{\Delta}=\sqrt{8228}=\sqrt{484*17}=\sqrt{484}*\sqrt{17}=22\sqrt{17}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-22\sqrt{17}}{2*16}=\frac{90-22\sqrt{17}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+22\sqrt{17}}{2*16}=\frac{90+22\sqrt{17}}{32}
$