1/4x+32=x

Solution for 1/4x+32=x equation:

1/4x+32=x

We move all terms to the left:

1/4x+32-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/4x+32=0

We multiply all the terms by the denominator


-1x*4x+32*4x+1=0

Wy multiply elements

-4x^2+128x+1=0

a = -4; b = 128; c = +1;
Δ = b2-4ac
Δ = 1282-4·(-4)·1
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-20\sqrt{41}}{2*-4}=\frac{-128-20\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+20\sqrt{41}}{2*-4}=\frac{-128+20\sqrt{41}}{-8}
$