1/5x+32=x

Solution for 1/5x+32=x equation:

1/5x+32=x

We move all terms to the left:

1/5x+32-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/5x+32=0

We multiply all the terms by the denominator


-1x*5x+32*5x+1=0

Wy multiply elements

-5x^2+160x+1=0

a = -5; b = 160; c = +1;
Δ = b2-4ac
Δ = 1602-4·(-5)·1
Δ = 25620
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:

$\sqrt{\Delta}=\sqrt{25620}=\sqrt{4*6405}=\sqrt{4}*\sqrt{6405}=2\sqrt{6405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-2\sqrt{6405}}{2*-5}=\frac{-160-2\sqrt{6405}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+2\sqrt{6405}}{2*-5}=\frac{-160+2\sqrt{6405}}{-10}
$