H(t)=-9.8t2+30t+1.5

Solution for H(t)=-9.8t2+30t+1.5 equation:

(H)=-9.8H^2+30H+1.5

We move all terms to the left:

(H)-(-9.8H^2+30H+1.5)=0

We get rid of parentheses

9.8H^2-30H+H-1.5=0

We add all the numbers together, and all the variables

9.8H^2-29H-1.5=0

a = 9.8; b = -29; c = -1.5;
Δ = b2-4ac
Δ = -292-4·9.8·(-1.5)
Δ = 899.8
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{-(-29)-\sqrt{899.8}}{2*9.8}=\frac{29-\sqrt{899.8}}{19.6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{899.8}}{2*9.8}=\frac{29+\sqrt{899.8}}{19.6}
$