16-1/2x=3/416x+1

Solution for 16-1/2x=3/416x+1 equation:

16-1/2x=3/416x+1

We move all terms to the left:

16-1/2x-(3/416x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 416x+1)!=0

x∈R


We get rid of parentheses

-1/2x-3/416x-1+16=0

We calculate fractions


(-416x)/832x^2+(-6x)/832x^2-1+16=0

We add all the numbers together, and all the variables

(-416x)/832x^2+(-6x)/832x^2+15=0

We multiply all the terms by the denominator


(-416x)+(-6x)+15*832x^2=0

Wy multiply elements

12480x^2+(-416x)+(-6x)=0

We get rid of parentheses

12480x^2-416x-6x=0

We add all the numbers together, and all the variables

12480x^2-422x=0

a = 12480; b = -422; c = 0;
Δ = b2-4ac
Δ = -4222-4·12480·0
Δ = 178084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{178084}=422$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-422)-422}{2*12480}=\frac{0}{24960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-422)+422}{2*12480}=\frac{844}{24960}
=211/6240
$