1/3h-4(2/3h-3)=2/3h-66

Solution for 1/3h-4(2/3h-3)=2/3h-66 equation:

1/3h-4(2/3h-3)=2/3h-66

We move all terms to the left:

1/3h-4(2/3h-3)-(2/3h-66)=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-66)!=0

h∈R


We multiply parentheses

1/3h-8h-(2/3h-66)+12=0

We get rid of parentheses

1/3h-8h-2/3h+66+12=0

We multiply all the terms by the denominator


-8h*3h+66*3h+12*3h+1-2=0

We add all the numbers together, and all the variables

-8h*3h+66*3h+12*3h-1=0

Wy multiply elements

-24h^2+198h+36h-1=0

We add all the numbers together, and all the variables

-24h^2+234h-1=0

a = -24; b = 234; c = -1;
Δ = b2-4ac
Δ = 2342-4·(-24)·(-1)
Δ = 54660
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:

$\sqrt{\Delta}=\sqrt{54660}=\sqrt{4*13665}=\sqrt{4}*\sqrt{13665}=2\sqrt{13665}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-2\sqrt{13665}}{2*-24}=\frac{-234-2\sqrt{13665}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+2\sqrt{13665}}{2*-24}=\frac{-234+2\sqrt{13665}}{-48}
$