(3/x)+(5/(2x))=12

Solution for (3/x)+(5/(2x))=12 equation:

(3/x)+(5/(2x))=12

We move all terms to the left:

(3/x)+(5/(2x))-(12)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/x)+(+5/2x)-12=0

We get rid of parentheses

3/x+5/2x-12=0

We calculate fractions


6x/2x^2+5x/2x^2-12=0

We multiply all the terms by the denominator


6x+5x-12*2x^2=0

We add all the numbers together, and all the variables

11x-12*2x^2=0

Wy multiply elements

-24x^2+11x=0

a = -24; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-24)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-24}=\frac{-22}{-48}
=11/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-24}=\frac{0}{-48}
=0
$