6-4x=-4/x

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

6-4x=-4/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-4x+4/x+6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-4x*x+4=0

Wy multiply elements

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

a = -4; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-4)·4
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*-4}=\frac{4}{-8}
=-1/2
$