3/x=15/2x+6

Solution for 3/x=15/2x+6 equation:

3/x=15/2x+6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

3/x-15/2x-6=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+6x+(-15x)=0

We get rid of parentheses

-12x^2+6x-15x=0

We add all the numbers together, and all the variables

-12x^2-9x=0

a = -12; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-12)·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*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-12}=\frac{18}{-24}
=-3/4
$