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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


4x/5x^2+(-10x)/5x^2-2+4=0

We add all the numbers together, and all the variables

4x/5x^2+(-10x)/5x^2+2=0

We multiply all the terms by the denominator


4x+(-10x)+2*5x^2=0

Wy multiply elements

10x^2+4x+(-10x)=0

We get rid of parentheses

10x^2+4x-10x=0

We add all the numbers together, and all the variables

10x^2-6x=0

a = 10; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·10·0
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{-(-6)-6}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*10}=\frac{12}{20}
=3/5
$