x=3-4/3x

Solution for x=3-4/3x equation:

x=3-4/3x

We move all terms to the left:

x-(3-4/3x)=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-(-4/3x+3)=0

We get rid of parentheses

x+4/3x-3=0

We multiply all the terms by the denominator


x*3x-3*3x+4=0

Wy multiply elements

3x^2-9x+4=0

a = 3; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·3·4
Δ = 33
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{-(-9)-\sqrt{33}}{2*3}=\frac{9-\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*3}=\frac{9+\sqrt{33}}{6}
$