392/x=x

Solution for 392/x=x equation:

392/x=x

We move all terms to the left:

392/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+392/x=0

We multiply all the terms by the denominator


-1x*x+392=0

Wy multiply elements

-1x^2+392=0

a = -1; b = 0; c = +392;
Δ = b2-4ac
Δ = 02-4·(-1)·392
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*-1}=\frac{0-28\sqrt{2}}{-2}
=-\frac{28\sqrt{2}}{-2}
=-\frac{14\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*-1}=\frac{0+28\sqrt{2}}{-2}
=\frac{28\sqrt{2}}{-2}
=\frac{14\sqrt{2}}{-1}
$