H(t)=-4.9t^2+75t+12

Solution for H(t)=-4.9t^2+75t+12 equation:

(H)=-4.9H^2+75H+12

We move all terms to the left:

(H)-(-4.9H^2+75H+12)=0

We get rid of parentheses

4.9H^2-75H+H-12=0

We add all the numbers together, and all the variables

4.9H^2-74H-12=0

a = 4.9; b = -74; c = -12;
Δ = b2-4ac
Δ = -742-4·4.9·(-12)
Δ = 5711.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-\sqrt{5711.2}}{2*4.9}=\frac{74-\sqrt{5711.2}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+\sqrt{5711.2}}{2*4.9}=\frac{74+\sqrt{5711.2}}{9.8}
$