4/3x=x+3

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

4/3x=x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-x-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 = 129
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{129}}{2*-3}=\frac{9-\sqrt{129}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*-3}=\frac{9+\sqrt{129}}{-6}
$