H=5t^2+110t

Solution for H=5t^2+110t equation:

=5H^2+110H

We move all terms to the left:

-(5H^2+110H)=0

We get rid of parentheses

-5H^2-110H=0

a = -5; b = -110; c = 0;
Δ = b2-4ac
Δ = -1102-4·(-5)·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-110}{2*-5}=\frac{0}{-10}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+110}{2*-5}=\frac{220}{-10}
=-22
$