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

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

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

We move all terms to the left:

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


Domain of the equation: 3x+3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x+2/3x-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-9x+2=0

a = 6; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·6·2
Δ = 33
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{33}}{2*6}=\frac{9-\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*6}=\frac{9+\sqrt{33}}{12}
$