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

Solution for 2/x+3/x-3+5/2x=0 equation:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


(6x+2)/2x^2+5x/2x^2-3=0

We multiply all the terms by the denominator


(6x+2)+5x-3*2x^2=0

We add all the numbers together, and all the variables

5x+(6x+2)-3*2x^2=0

Wy multiply elements

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

We get rid of parentheses

-6x^2+5x+6x+2=0

We add all the numbers together, and all the variables

-6x^2+11x+2=0

a = -6; b = 11; c = +2;
Δ = b2-4ac
Δ = 112-4·(-6)·2
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*-6}=\frac{2}{-12}
=-1/6
$