h(3h+4)=4+8h

Solution for h(3h+4)=4+8h equation:

h(3h+4)=4+8h

We move all terms to the left:

h(3h+4)-(4+8h)=0

We add all the numbers together, and all the variables

h(3h+4)-(8h+4)=0

We multiply parentheses

3h^2+4h-(8h+4)=0

We get rid of parentheses

3h^2+4h-8h-4=0

We add all the numbers together, and all the variables

3h^2-4h-4=0

a = 3; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·3·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*3}=\frac{-4}{6}
=-2/3
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*3}=\frac{12}{6}
=2
$