H=-49t^2+49t+1.5=124

Solution for H=-49t^2+49t+1.5=124 equation:

=-49H^2+49H+1.5=124

We move all terms to the left:

-(-49H^2+49H+1.5)=0

We get rid of parentheses

49H^2-49H-1.5=0

a = 49; b = -49; c = -1.5;
Δ = b2-4ac
Δ = -492-4·49·(-1.5)
Δ = 2695
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2695}=\sqrt{49*55}=\sqrt{49}*\sqrt{55}=7\sqrt{55}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-7\sqrt{55}}{2*49}=\frac{49-7\sqrt{55}}{98}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+7\sqrt{55}}{2*49}=\frac{49+7\sqrt{55}}{98}
$