H=175-16t^2

Solution for H=175-16t^2 equation:

=175-16H^2

We move all terms to the left:

-(175-16H^2)=0

We get rid of parentheses

16H^2-175=0

a = 16; b = 0; c = -175;
Δ = b2-4ac
Δ = 02-4·16·(-175)
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{7}}{2*16}=\frac{0-40\sqrt{7}}{32}
=-\frac{40\sqrt{7}}{32}
=-\frac{5\sqrt{7}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{7}}{2*16}=\frac{0+40\sqrt{7}}{32}
=\frac{40\sqrt{7}}{32}
=\frac{5\sqrt{7}}{4}
$