H=12+15t+-16t2

Solution for H=12+15t+-16t2 equation:

=12+15H+-16H^2

We move all terms to the left:

-(12+15H+-16H^2)=0

We use the square of the difference formula

-(12+15H-16H^2)=0

We get rid of parentheses

16H^2-15H-12=0

a = 16; b = -15; c = -12;
Δ = b2-4ac
Δ = -152-4·16·(-12)
Δ = 993
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{-(-15)-\sqrt{993}}{2*16}=\frac{15-\sqrt{993}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{993}}{2*16}=\frac{15+\sqrt{993}}{32}
$