6h(h+4)=42-3h

Solution for 6h(h+4)=42-3h equation:

6h(h+4)=42-3h

We move all terms to the left:

6h(h+4)-(42-3h)=0

We add all the numbers together, and all the variables

6h(h+4)-(-3h+42)=0

We multiply parentheses

6h^2+24h-(-3h+42)=0

We get rid of parentheses

6h^2+24h+3h-42=0

We add all the numbers together, and all the variables

6h^2+27h-42=0

a = 6; b = 27; c = -42;
Δ = b2-4ac
Δ = 272-4·6·(-42)
Δ = 1737
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1737}=\sqrt{9*193}=\sqrt{9}*\sqrt{193}=3\sqrt{193}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{193}}{2*6}=\frac{-27-3\sqrt{193}}{12}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{193}}{2*6}=\frac{-27+3\sqrt{193}}{12}
$