12/x+4=9/2x

Solution for 12/x+4=9/2x equation:

12/x+4=9/2x

We move all terms to the left:

12/x+4-(9/2x)=0


Domain of the equation: 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

12/x-(+9/2x)+4=0

We get rid of parentheses

12/x-9/2x+4=0

We calculate fractions


24x/2x^2+(-9x)/2x^2+4=0

We multiply all the terms by the denominator


24x+(-9x)+4*2x^2=0

Wy multiply elements

8x^2+24x+(-9x)=0

We get rid of parentheses

8x^2+24x-9x=0

We add all the numbers together, and all the variables

8x^2+15x=0

a = 8; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·8·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*8}=\frac{-30}{16}
=-1+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*8}=\frac{0}{16}
=0
$