16/x-2=12x/2x

Solution for 16/x-2=12x/2x equation:

16/x-2=12x/2x

We move all terms to the left:

16/x-2-(12x/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

16/x-(+12x/2x)-2=0

We get rid of parentheses

16/x-12x/2x-2=0

We calculate fractions


(-12x^2)/2x^2+32x/2x^2-2=0

We multiply all the terms by the denominator


(-12x^2)+32x-2*2x^2=0

Wy multiply elements

(-12x^2)-4x^2+32x=0

We get rid of parentheses

-12x^2-4x^2+32x=0

We add all the numbers together, and all the variables

-16x^2+32x=0

a = -16; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-16)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-16}=\frac{-64}{-32}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-16}=\frac{0}{-32}
=0
$