1/3h-4(2/3h-3)=5/3h-6

Solution for 1/3h-4(2/3h-3)=5/3h-6 equation:

1/3h-4(2/3h-3)=5/3h-6

We move all terms to the left:

1/3h-4(2/3h-3)-(5/3h-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-(5/3h-6)+12=0

We get rid of parentheses

1/3h-8h-5/3h+6+12=0

We multiply all the terms by the denominator


-8h*3h+6*3h+12*3h+1-5=0

We add all the numbers together, and all the variables

-8h*3h+6*3h+12*3h-4=0

Wy multiply elements

-24h^2+18h+36h-4=0

We add all the numbers together, and all the variables

-24h^2+54h-4=0

a = -24; b = 54; c = -4;
Δ = b2-4ac
Δ = 542-4·(-24)·(-4)
Δ = 2532
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:

$\sqrt{\Delta}=\sqrt{2532}=\sqrt{4*633}=\sqrt{4}*\sqrt{633}=2\sqrt{633}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{633}}{2*-24}=\frac{-54-2\sqrt{633}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{633}}{2*-24}=\frac{-54+2\sqrt{633}}{-48}
$