3/x+2=15/2x-3

Solution for 3/x+2=15/2x-3 equation:

3/x+2=15/2x-3

We move all terms to the left:

3/x+2-(15/2x-3)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

3/x-15/2x+3+2=0

We calculate fractions


6x/2x^2+(-15x)/2x^2+3+2=0

We add all the numbers together, and all the variables

6x/2x^2+(-15x)/2x^2+5=0

We multiply all the terms by the denominator


6x+(-15x)+5*2x^2=0

Wy multiply elements

10x^2+6x+(-15x)=0

We get rid of parentheses

10x^2+6x-15x=0

We add all the numbers together, and all the variables

10x^2-9x=0

a = 10; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·10·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*10}=\frac{18}{20}
=9/10
$