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

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

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

We move all terms to the left:

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


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

h∈R



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

h∈R


We multiply parentheses

3h-8h-(2/3h-6)+12=0

We get rid of parentheses

3h-8h-2/3h+6+12=0

We multiply all the terms by the denominator


3h*3h-8h*3h+6*3h+12*3h-2=0

Wy multiply elements

9h^2-24h^2+18h+36h-2=0

We add all the numbers together, and all the variables

-15h^2+54h-2=0

a = -15; b = 54; c = -2;
Δ = b2-4ac
Δ = 542-4·(-15)·(-2)
Δ = 2796
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:

$\sqrt{\Delta}=\sqrt{2796}=\sqrt{4*699}=\sqrt{4}*\sqrt{699}=2\sqrt{699}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{699}}{2*-15}=\frac{-54-2\sqrt{699}}{-30}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{699}}{2*-15}=\frac{-54+2\sqrt{699}}{-30}
$