5/x-2=3x

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

5/x-2=3x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+5/x-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -3; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-3)·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*-3}=\frac{10}{-6}
=-1+2/3
$