H3+3h2+3h=7

Solution for H3+3h2+3h=7 equation:

3+3H^2+3H=7

We move all terms to the left:

3+3H^2+3H-(7)=0

We add all the numbers together, and all the variables

3H^2+3H-4=0

a = 3; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·3·(-4)
Δ = 57
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{-(3)-\sqrt{57}}{2*3}=\frac{-3-\sqrt{57}}{6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*3}=\frac{-3+\sqrt{57}}{6}
$