3x-5/3x+2=2

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

3x-5/3x+2=2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x-5/3x=0

We multiply all the terms by the denominator


3x*3x-5=0

Wy multiply elements

9x^2-5=0

a = 9; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·9·(-5)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*9}=\frac{0-6\sqrt{5}}{18}
=-\frac{6\sqrt{5}}{18}
=-\frac{\sqrt{5}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*9}=\frac{0+6\sqrt{5}}{18}
=\frac{6\sqrt{5}}{18}
=\frac{\sqrt{5}}{3}
$