1/3h-4(2/3h-3)=2/3h-8

Solution for 1/3h-4(2/3h-3)=2/3h-8 equation:

1/3h-4(2/3h-3)=2/3h-8

We move all terms to the left:

1/3h-4(2/3h-3)-(2/3h-8)=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-8)!=0

h∈R


We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-24h^2+60h-1=0

a = -24; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·(-24)·(-1)
Δ = 3504
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:

$\sqrt{\Delta}=\sqrt{3504}=\sqrt{16*219}=\sqrt{16}*\sqrt{219}=4\sqrt{219}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{219}}{2*-24}=\frac{-60-4\sqrt{219}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{219}}{2*-24}=\frac{-60+4\sqrt{219}}{-48}
$