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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+15x+6x+2=0

We add all the numbers together, and all the variables

-3x^2+21x+2=0

a = -3; b = 21; c = +2;
Δ = b2-4ac
Δ = 212-4·(-3)·2
Δ = 465
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{-(21)-\sqrt{465}}{2*-3}=\frac{-21-\sqrt{465}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{465}}{2*-3}=\frac{-21+\sqrt{465}}{-6}
$