4/3x+29=x

Solution for 4/3x+29=x equation:

4/3x+29=x

We move all terms to the left:

4/3x+29-(x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/3x+29=0

We multiply all the terms by the denominator


-1x*3x+29*3x+4=0

Wy multiply elements

-3x^2+87x+4=0

a = -3; b = 87; c = +4;
Δ = b2-4ac
Δ = 872-4·(-3)·4
Δ = 7617
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{-(87)-\sqrt{7617}}{2*-3}=\frac{-87-\sqrt{7617}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+\sqrt{7617}}{2*-3}=\frac{-87+\sqrt{7617}}{-6}
$