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

Solution for (1)/(3)h-4((2)/(3)h-3)=(2)/(3)h-6 equation:

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

We move all terms to the left:

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


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



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

h∈R



Domain of the equation: 3h-6)!=0

h∈R


We multiply parentheses

1/3h-8h-(2/3h-6)+12=0

We get rid of parentheses

1/3h-8h-2/3h+6+12=0

We multiply all the terms by the denominator


-8h*3h+6*3h+12*3h+1-2=0

We add all the numbers together, and all the variables

-8h*3h+6*3h+12*3h-1=0

Wy multiply elements

-24h^2+18h+36h-1=0

We add all the numbers together, and all the variables

-24h^2+54h-1=0

a = -24; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·(-24)·(-1)
Δ = 2820
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:

$\sqrt{\Delta}=\sqrt{2820}=\sqrt{4*705}=\sqrt{4}*\sqrt{705}=2\sqrt{705}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{705}}{2*-24}=\frac{-54-2\sqrt{705}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{705}}{2*-24}=\frac{-54+2\sqrt{705}}{-48}
$