2x+5x/3x-1=2

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

2x+5x/3x-1=2

We move all terms to the left:

2x+5x/3x-1-(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

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2+5x-9x=0

We add all the numbers together, and all the variables

6x^2-4x=0

a = 6; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·6·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*6}=\frac{8}{12}
=2/3
$