X-3/x=-2x

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

X-3/X=-2X

We move all terms to the left:

X-3/X-(-2X)=0


Domain of the equation: X!=0

X∈R


We get rid of parentheses

X-3/X+2X=0

We multiply all the terms by the denominator


X*X+2X*X-3=0

Wy multiply elements

X^2+2X^2-3=0

We add all the numbers together, and all the variables

3X^2-3=0

a = 3; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·3·(-3)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*3}=\frac{-6}{6}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*3}=\frac{6}{6}
=1
$