H(t)=-6.5t^2+50t

Solution for H(t)=-6.5t^2+50t equation:

(H)=-6.5H^2+50H

We move all terms to the left:

(H)-(-6.5H^2+50H)=0

We get rid of parentheses

6.5H^2-50H+H=0

We add all the numbers together, and all the variables

6.5H^2-49H=0

a = 6.5; b = -49; c = 0;
Δ = b2-4ac
Δ = -492-4·6.5·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-49}{2*6.5}=\frac{0}{13}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+49}{2*6.5}=\frac{98}{13}
=7+7/13
$