3/x-2=5x

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

3/x-2=5x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+3/x-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -5; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-5)·3
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*-5}=\frac{-6}{-10}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*-5}=\frac{10}{-10}
=-1
$