X=117+2/3x

Solution for X=117+2/3x equation:

X=117+2/3X

We move all terms to the left:

X-(117+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+117)=0

We get rid of parentheses

X-2/3X-117=0

We multiply all the terms by the denominator


X*3X-117*3X-2=0

Wy multiply elements

3X^2-351X-2=0

a = 3; b = -351; c = -2;
Δ = b2-4ac
Δ = -3512-4·3·(-2)
Δ = 123225
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:

$\sqrt{\Delta}=\sqrt{123225}=\sqrt{25*4929}=\sqrt{25}*\sqrt{4929}=5\sqrt{4929}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-351)-5\sqrt{4929}}{2*3}=\frac{351-5\sqrt{4929}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-351)+5\sqrt{4929}}{2*3}=\frac{351+5\sqrt{4929}}{6}
$