5x/2x=8/x+2

Solution for 5x/2x=8/x+2 equation:

5x/2x=8/x+2

We move all terms to the left:

5x/2x-(8/x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

5x/2x-8/x-2=0

We calculate fractions


5x^2/2x^2+(-16x)/2x^2-2=0

We multiply all the terms by the denominator


5x^2+(-16x)-2*2x^2=0

Wy multiply elements

5x^2-4x^2+(-16x)=0

We get rid of parentheses

5x^2-4x^2-16x=0

We add all the numbers together, and all the variables

x^2-16x=0

a = 1; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·1·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*1}=\frac{32}{2}
=16
$