1/3h-4(2/3h-3)=2/3h-9

Solution for 1/3h-4(2/3h-3)=2/3h-9 equation:

1/3h-4(2/3h-3)=2/3h-9

We move all terms to the left:

1/3h-4(2/3h-3)-(2/3h-9)=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-9)!=0

h∈R


We multiply parentheses

1/3h-8h-(2/3h-9)+12=0

We get rid of parentheses

1/3h-8h-2/3h+9+12=0

We multiply all the terms by the denominator


-8h*3h+9*3h+12*3h+1-2=0

We add all the numbers together, and all the variables

-8h*3h+9*3h+12*3h-1=0

Wy multiply elements

-24h^2+27h+36h-1=0

We add all the numbers together, and all the variables

-24h^2+63h-1=0

a = -24; b = 63; c = -1;
Δ = b2-4ac
Δ = 632-4·(-24)·(-1)
Δ = 3873
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-\sqrt{3873}}{2*-24}=\frac{-63-\sqrt{3873}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+\sqrt{3873}}{2*-24}=\frac{-63+\sqrt{3873}}{-48}
$