x=9/32x

Solution for x=9/32x equation:

x=9/32x

We move all terms to the left:

x-(9/32x)=0


Domain of the equation: 32x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+9/32x)=0

We get rid of parentheses

x-9/32x=0

We multiply all the terms by the denominator


x*32x-9=0

Wy multiply elements

32x^2-9=0

a = 32; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·32·(-9)
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*32}=\frac{0-24\sqrt{2}}{64}
=-\frac{24\sqrt{2}}{64}
=-\frac{3\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*32}=\frac{0+24\sqrt{2}}{64}
=\frac{24\sqrt{2}}{64}
=\frac{3\sqrt{2}}{8}
$