2/3x-5=4+x

Solution for 2/3x-5=4+x equation:

2/3x-5=4+x

We move all terms to the left:

2/3x-5-(4+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

2/3x-(x+4)-5=0

We get rid of parentheses

2/3x-x-4-5=0

We multiply all the terms by the denominator


-x*3x-4*3x-5*3x+2=0

Wy multiply elements

-3x^2-12x-15x+2=0

We add all the numbers together, and all the variables

-3x^2-27x+2=0

a = -3; b = -27; c = +2;
Δ = b2-4ac
Δ = -272-4·(-3)·2
Δ = 753
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{-(-27)-\sqrt{753}}{2*-3}=\frac{27-\sqrt{753}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{753}}{2*-3}=\frac{27+\sqrt{753}}{-6}
$