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

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

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

We move all terms to the left:

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


Domain of the equation: 3h!=0

h!=0/3

h!=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)-(+2/3h)-6=0

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -24; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·(-24)·(-1)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{57}}{2*-24}=\frac{18-2\sqrt{57}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{57}}{2*-24}=\frac{18+2\sqrt{57}}{-48}
$