5/x-2x/1=2x/x+3

Solution for 5/x-2x/1=2x/x+3 equation:

5/x-2x/1=2x/x+3

We move all terms to the left:

5/x-2x/1-(2x/x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

5/x-2x/1-2x/x-3=0

We calculate fractions


(-2x^2)/x+(-2x+5)/x-3=0

We multiply all the terms by the denominator


(-2x^2)+(-2x+5)-3*x=0

We add all the numbers together, and all the variables

(-2x^2)-3x+(-2x+5)=0

We get rid of parentheses

-2x^2-3x-2x+5=0

We add all the numbers together, and all the variables

-2x^2-5x+5=0

a = -2; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-2)·5
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{65}}{2*-2}=\frac{5-\sqrt{65}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*-2}=\frac{5+\sqrt{65}}{-4}
$