289/x=x

Solution for 289/x=x equation:

289/x=x

We move all terms to the left:

289/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+289/x=0

We multiply all the terms by the denominator


-1x*x+289=0

Wy multiply elements

-1x^2+289=0

a = -1; b = 0; c = +289;
Δ = b2-4ac
Δ = 02-4·(-1)·289
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34}{2*-1}=\frac{-34}{-2}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34}{2*-1}=\frac{34}{-2}
=-17
$