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

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

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

We move all terms to the left:

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


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



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

h∈R



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

h∈R


We multiply parentheses

1/3h-8h-(2/3h-6)+16=0

We get rid of parentheses

1/3h-8h-2/3h+6+16=0

We multiply all the terms by the denominator


-8h*3h+6*3h+16*3h+1-2=0

We add all the numbers together, and all the variables

-8h*3h+6*3h+16*3h-1=0

Wy multiply elements

-24h^2+18h+48h-1=0

We add all the numbers together, and all the variables

-24h^2+66h-1=0

a = -24; b = 66; c = -1;
Δ = b2-4ac
Δ = 662-4·(-24)·(-1)
Δ = 4260
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:

$\sqrt{\Delta}=\sqrt{4260}=\sqrt{4*1065}=\sqrt{4}*\sqrt{1065}=2\sqrt{1065}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1065}}{2*-24}=\frac{-66-2\sqrt{1065}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1065}}{2*-24}=\frac{-66+2\sqrt{1065}}{-48}
$