1/x-2=3x

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

1/x-2=3x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/x-2=0

We multiply all the terms by the denominator


-3x*x-2*x+1=0

We add all the numbers together, and all the variables

-2x-3x*x+1=0

Wy multiply elements

-3x^2-2x+1=0

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