2=1/3h-3-3-4h

Solution for 2=1/3h-3-3-4h equation:

2=1/3h-3-3-4h

We move all terms to the left:

2-(1/3h-3-3-4h)=0


Domain of the equation: 3h-3-3-4h)!=0

We move all terms containing h to the left, all other terms to the right

3h-4h)!=6

h∈R


We add all the numbers together, and all the variables

-(-4h+1/3h-6)+2=0

We get rid of parentheses

4h-1/3h+6+2=0

We multiply all the terms by the denominator


4h*3h+6*3h+2*3h-1=0

Wy multiply elements

12h^2+18h+6h-1=0

We add all the numbers together, and all the variables

12h^2+24h-1=0

a = 12; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·12·(-1)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{39}}{2*12}=\frac{-24-4\sqrt{39}}{24}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{39}}{2*12}=\frac{-24+4\sqrt{39}}{24}
$