5x/x-3x=2

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

5x/x-3x=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x-3x*x=0

Wy multiply elements

-3x^2+3x=0

a = -3; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-3)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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