1/2x-3=3/x+4

Solution for 1/2x-3=3/x+4 equation:

1/2x-3=3/x+4

We move all terms to the left:

1/2x-3-(3/x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+4)!=0

x∈R


We get rid of parentheses

1/2x-3/x-4-3=0

We calculate fractions


x/2x^2+(-6x)/2x^2-4-3=0

We add all the numbers together, and all the variables

x/2x^2+(-6x)/2x^2-7=0

We multiply all the terms by the denominator


x+(-6x)-7*2x^2=0

Wy multiply elements

-14x^2+x+(-6x)=0

We get rid of parentheses

-14x^2+x-6x=0

We add all the numbers together, and all the variables

-14x^2-5x=0

a = -14; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-14)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-14}=\frac{0}{-28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-14}=\frac{10}{-28}
=-5/14
$