H=560+32t+-16t2

Solution for H=560+32t+-16t2 equation:

=560+32H+-16H^2

We move all terms to the left:

-(560+32H+-16H^2)=0

We use the square of the difference formula

-(560+32H-16H^2)=0

We get rid of parentheses

16H^2-32H-560=0

a = 16; b = -32; c = -560;
Δ = b2-4ac
Δ = -322-4·16·(-560)
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-192}{2*16}=\frac{-160}{32}
=-5
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+192}{2*16}=\frac{224}{32}
=7
$