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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/2x^2+(-3x)/2x^2-3-2=0

We add all the numbers together, and all the variables

10x/2x^2+(-3x)/2x^2-5=0

We multiply all the terms by the denominator


10x+(-3x)-5*2x^2=0

Wy multiply elements

-10x^2+10x+(-3x)=0

We get rid of parentheses

-10x^2+10x-3x=0

We add all the numbers together, and all the variables

-10x^2+7x=0

a = -10; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-10)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-10}=\frac{-14}{-20}
=7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-10}=\frac{0}{-20}
=0
$