5x-1/3x+2=2

Solution for 5x-1/3x+2=2 equation:

5x-1/3x+2=2

We move all terms to the left:

5x-1/3x+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

5x-1/3x=0

We multiply all the terms by the denominator


5x*3x-1=0

Wy multiply elements

15x^2-1=0

a = 15; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·15·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*15}=\frac{0-2\sqrt{15}}{30}
=-\frac{2\sqrt{15}}{30}
=-\frac{\sqrt{15}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*15}=\frac{0+2\sqrt{15}}{30}
=\frac{2\sqrt{15}}{30}
=\frac{\sqrt{15}}{15}
$