H=70t+5t^2

Solution for H=70t+5t^2 equation:

=70H+5H^2

We move all terms to the left:

-(70H+5H^2)=0

We get rid of parentheses

-5H^2-70H=0

a = -5; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·(-5)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*-5}=\frac{0}{-10}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*-5}=\frac{140}{-10}
=-14
$