3h+12(2h+6)3h+12(2h+6)=4h+3

Solution for 3h+12(2h+6)3h+12(2h+6)=4h+3 equation:

3h+12(2h+6)3h+12(2h+6)=4h+3

We move all terms to the left:

3h+12(2h+6)3h+12(2h+6)-(4h+3)=0

We multiply parentheses

72h^2+3h+216h+24h-(4h+3)+72=0

We get rid of parentheses

72h^2+3h+216h+24h-4h-3+72=0

We add all the numbers together, and all the variables

72h^2+239h+69=0

a = 72; b = 239; c = +69;
Δ = b2-4ac
Δ = 2392-4·72·69
Δ = 37249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{37249}=193$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(239)-193}{2*72}=\frac{-432}{144}
=-3
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(239)+193}{2*72}=\frac{-46}{144}
=-23/72
$