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

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

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

We move all terms to the left:

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

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -24; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-24)·(-1)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-20\sqrt{3}}{2*-24}=\frac{-36-20\sqrt{3}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+20\sqrt{3}}{2*-24}=\frac{-36+20\sqrt{3}}{-48}
$