H=12t+3t2

Solution for H=12t+3t2 equation:

=12H+3H^2

We move all terms to the left:

-(12H+3H^2)=0

We get rid of parentheses

-3H^2-12H=0

a = -3; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-3)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-3}=\frac{0}{-6}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-3}=\frac{24}{-6}
=-4
$