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

Solution for 1/3x+2/3x=5+2x equation:

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-6x^2-15x+3=0

a = -6; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·(-6)·3
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{33}}{2*-6}=\frac{15-3\sqrt{33}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{33}}{2*-6}=\frac{15+3\sqrt{33}}{-12}
$