X=167-7/3x

Solution for X=167-7/3x equation:

X=167-7/3X

We move all terms to the left:

X-(167-7/3X)=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-(-7/3X+167)=0

We get rid of parentheses

X+7/3X-167=0

We multiply all the terms by the denominator


X*3X-167*3X+7=0

Wy multiply elements

3X^2-501X+7=0

a = 3; b = -501; c = +7;
Δ = b2-4ac
Δ = -5012-4·3·7
Δ = 250917
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{-(-501)-\sqrt{250917}}{2*3}=\frac{501-\sqrt{250917}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-501)+\sqrt{250917}}{2*3}=\frac{501+\sqrt{250917}}{6}
$