X=10-2/3x

Solution for X=10-2/3x equation:

X=10-2/3X

We move all terms to the left:

X-(10-2/3X)=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+10)=0

We get rid of parentheses

X+2/3X-10=0

We multiply all the terms by the denominator


X*3X-10*3X+2=0

Wy multiply elements

3X^2-30X+2=0

a = 3; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·3·2
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*3}=\frac{30-2\sqrt{219}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*3}=\frac{30+2\sqrt{219}}{6}
$