H=4+45t-16t2

Solution for H=4+45t-16t2 equation:

=4+45H-16H^2

We move all terms to the left:

-(4+45H-16H^2)=0

We get rid of parentheses

16H^2-45H-4=0

a = 16; b = -45; c = -4;
Δ = b2-4ac
Δ = -452-4·16·(-4)
Δ = 2281
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{-(-45)-\sqrt{2281}}{2*16}=\frac{45-\sqrt{2281}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2281}}{2*16}=\frac{45+\sqrt{2281}}{32}
$