9x/32x+16=1/x

Solution for 9x/32x+16=1/x equation:

9x/32x+16=1/x

We move all terms to the left:

9x/32x+16-(1/x)=0


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x/32x-(+1/x)+16=0

We get rid of parentheses

9x/32x-1/x+16=0

We calculate fractions


9x^2/32x^2+(-32x)/32x^2+16=0

We multiply all the terms by the denominator


9x^2+(-32x)+16*32x^2=0

Wy multiply elements

9x^2+512x^2+(-32x)=0

We get rid of parentheses

9x^2+512x^2-32x=0

We add all the numbers together, and all the variables

521x^2-32x=0

a = 521; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·521·0
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*521}=\frac{0}{1042}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*521}=\frac{64}{1042}
=32/521
$