2/3*x-x+29=0

Solution for 2/3*x-x+29=0 equation:

2/3x-x+29=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+2/3x+29=0

We multiply all the terms by the denominator


-1x*3x+29*3x+2=0

Wy multiply elements

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

a = -3; b = 87; c = +2;
Δ = b2-4ac
Δ = 872-4·(-3)·2
Δ = 7593
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{7593}}{2*-3}=\frac{-87-\sqrt{7593}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+\sqrt{7593}}{2*-3}=\frac{-87+\sqrt{7593}}{-6}
$