3x+2-x=-2/3x+26

Solution for 3x+2-x=-2/3x+26 equation:

3x+2-x=-2/3x+26

We move all terms to the left:

3x+2-x-(-2/3x+26)=0


Domain of the equation: 3x+26)!=0

x∈R


We add all the numbers together, and all the variables

2x-(-2/3x+26)+2=0

We get rid of parentheses

2x+2/3x-26+2=0

We multiply all the terms by the denominator


2x*3x-26*3x+2*3x+2=0

Wy multiply elements

6x^2-78x+6x+2=0

We add all the numbers together, and all the variables

6x^2-72x+2=0

a = 6; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·6·2
Δ = 5136
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:

$\sqrt{\Delta}=\sqrt{5136}=\sqrt{16*321}=\sqrt{16}*\sqrt{321}=4\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{321}}{2*6}=\frac{72-4\sqrt{321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{321}}{2*6}=\frac{72+4\sqrt{321}}{12}
$