5/x-4=2/4x+2

Solution for 5/x-4=2/4x+2 equation:

5/x-4=2/4x+2

We move all terms to the left:

5/x-4-(2/4x+2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

5/x-2/4x-2-4=0

We calculate fractions


20x/4x^2+(-2x)/4x^2-2-4=0

We add all the numbers together, and all the variables

20x/4x^2+(-2x)/4x^2-6=0

We multiply all the terms by the denominator


20x+(-2x)-6*4x^2=0

Wy multiply elements

-24x^2+20x+(-2x)=0

We get rid of parentheses

-24x^2+20x-2x=0

We add all the numbers together, and all the variables

-24x^2+18x=0

a = -24; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-24)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-24}=\frac{-36}{-48}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-24}=\frac{0}{-48}
=0
$