2/3x-4=x+3

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

2/3x-4=x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2-9x-12x+2=0

We add all the numbers together, and all the variables

-3x^2-21x+2=0

a = -3; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·(-3)·2
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{465}}{2*-3}=\frac{21-\sqrt{465}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{465}}{2*-3}=\frac{21+\sqrt{465}}{-6}
$