35+.125/x=x

Solution for 35+.125/x=x equation:

35+.125/x=x

We move all terms to the left:

35+.125/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+.125/x+35=0

We multiply all the terms by the denominator


-1x*x+35*x+.125=0

We add all the numbers together, and all the variables

35x-1x*x+0.125=0

Wy multiply elements

-1x^2+35x+0.125=0

a = -1; b = 35; c = +0.125;
Δ = b2-4ac
Δ = 352-4·(-1)·0.125
Δ = 1225.5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1225.5}}{2*-1}=\frac{-35-\sqrt{1225.5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1225.5}}{2*-1}=\frac{-35+\sqrt{1225.5}}{-2}
$