H=6t^2+25t+6

Solution for H=6t^2+25t+6 equation:

=6H^2+25H+6

We move all terms to the left:

-(6H^2+25H+6)=0

We get rid of parentheses

-6H^2-25H-6=0

a = -6; b = -25; c = -6;
Δ = b2-4ac
Δ = -252-4·(-6)·(-6)
Δ = 481
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{-(-25)-\sqrt{481}}{2*-6}=\frac{25-\sqrt{481}}{-12}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{481}}{2*-6}=\frac{25+\sqrt{481}}{-12}
$