12/x-12=-3/2x

Solution for 12/x-12=-3/2x equation:

12/x-12=-3/2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


24x/2x^2+3x/2x^2-12=0

We multiply all the terms by the denominator


24x+3x-12*2x^2=0

We add all the numbers together, and all the variables

27x-12*2x^2=0

Wy multiply elements

-24x^2+27x=0

a = -24; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-24)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-24}=\frac{-54}{-48}
=1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-24}=\frac{0}{-48}
=0
$