2/2x=3/x+16

Solution for 2/2x=3/x+16 equation:

2/2x=3/x+16

We move all terms to the left:

2/2x-(3/x+16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+16)!=0

x∈R


We get rid of parentheses

2/2x-3/x-16=0

We calculate fractions


2x/2x^2+(-6x)/2x^2-16=0

We multiply all the terms by the denominator


2x+(-6x)-16*2x^2=0

Wy multiply elements

-32x^2+2x+(-6x)=0

We get rid of parentheses

-32x^2+2x-6x=0

We add all the numbers together, and all the variables

-32x^2-4x=0

a = -32; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-32)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-32}=\frac{8}{-64}
=-1/8
$