H(t)=-49t^2+147t

Solution for H(t)=-49t^2+147t equation:

(H)=-49H^2+147H

We move all terms to the left:

(H)-(-49H^2+147H)=0

We get rid of parentheses

49H^2-147H+H=0

We add all the numbers together, and all the variables

49H^2-146H=0

a = 49; b = -146; c = 0;
Δ = b2-4ac
Δ = -1462-4·49·0
Δ = 21316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21316}=146$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-146)-146}{2*49}=\frac{0}{98}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-146)+146}{2*49}=\frac{292}{98}
=2+48/49
$