5/2x+3=4/x-2

Solution for 5/2x+3=4/x-2 equation:

5/2x+3=4/x-2

We move all terms to the left:

5/2x+3-(4/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

5/2x-4/x+2+3=0

We calculate fractions


5x/2x^2+(-8x)/2x^2+2+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


5x+(-8x)+5*2x^2=0

Wy multiply elements

10x^2+5x+(-8x)=0

We get rid of parentheses

10x^2+5x-8x=0

We add all the numbers together, and all the variables

10x^2-3x=0

a = 10; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·10·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*10}=\frac{6}{20}
=3/10
$