2/3x-4=-3x+6

Solution for 2/3x-4=-3x+6 equation:

2/3x-4=-3x+6

We move all terms to the left:

2/3x-4-(-3x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x+3x-6-4=0

We multiply all the terms by the denominator


3x*3x-6*3x-4*3x+2=0

Wy multiply elements

9x^2-18x-12x+2=0

We add all the numbers together, and all the variables

9x^2-30x+2=0

a = 9; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·9·2
Δ = 828
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{23}}{2*9}=\frac{30-6\sqrt{23}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{23}}{2*9}=\frac{30+6\sqrt{23}}{18}
$