6/x=2x-4

Solution for 6/x=2x-4 equation:

6/x=2x-4

We move all terms to the left:

6/x-(2x-4)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

6/x-2x+4=0

We multiply all the terms by the denominator


-2x*x+4*x+6=0

We add all the numbers together, and all the variables

4x-2x*x+6=0

Wy multiply elements

-2x^2+4x+6=0

a = -2; b = 4; c = +6;
Δ = b2-4ac
Δ = 42-4·(-2)·6
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{-(4)-8}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-2}=\frac{4}{-4}
=-1
$