H=-16t^2+85t+1/12

Solution for H=-16t^2+85t+1/12 equation:

=-16H^2+85H+1/12

We move all terms to the left:

-(-16H^2+85H+1/12)=0

We get rid of parentheses

16H^2-85H-1/12=0

We multiply all the terms by the denominator


16H^2*12-85H*12-1=0

Wy multiply elements

192H^2-1020H-1=0

a = 192; b = -1020; c = -1;
Δ = b2-4ac
Δ = -10202-4·192·(-1)
Δ = 1041168
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:

$\sqrt{\Delta}=\sqrt{1041168}=\sqrt{16*65073}=\sqrt{16}*\sqrt{65073}=4\sqrt{65073}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1020)-4\sqrt{65073}}{2*192}=\frac{1020-4\sqrt{65073}}{384}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1020)+4\sqrt{65073}}{2*192}=\frac{1020+4\sqrt{65073}}{384}
$