2/3x+3x=-x+5

Solution for 2/3x+3x=-x+5 equation:

2/3x+3x=-x+5

We move all terms to the left:

2/3x+3x-(-x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+3x-(-1x+5)=0

We add all the numbers together, and all the variables

3x+2/3x-(-1x+5)=0

We get rid of parentheses

3x+2/3x+1x-5=0

We multiply all the terms by the denominator


3x*3x+1x*3x-5*3x+2=0

Wy multiply elements

9x^2+3x^2-15x+2=0

We add all the numbers together, and all the variables

12x^2-15x+2=0

a = 12; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·12·2
Δ = 129
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{-(-15)-\sqrt{129}}{2*12}=\frac{15-\sqrt{129}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{129}}{2*12}=\frac{15+\sqrt{129}}{24}
$