x=26+2/3*x

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

x=26+2/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-2/3x-26=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-78x-2=0

a = 3; b = -78; c = -2;
Δ = b2-4ac
Δ = -782-4·3·(-2)
Δ = 6108
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:

$\sqrt{\Delta}=\sqrt{6108}=\sqrt{4*1527}=\sqrt{4}*\sqrt{1527}=2\sqrt{1527}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1527}}{2*3}=\frac{78-2\sqrt{1527}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1527}}{2*3}=\frac{78+2\sqrt{1527}}{6}
$