91/x=x

Solution for 91/x=x equation:

91/x=x

We move all terms to the left:

91/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+91/x=0

We multiply all the terms by the denominator


-1x*x+91=0

Wy multiply elements

-1x^2+91=0

a = -1; b = 0; c = +91;
Δ = b2-4ac
Δ = 02-4·(-1)·91
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{91}}{2*-1}=\frac{0-2\sqrt{91}}{-2}
=-\frac{2\sqrt{91}}{-2}
=-\frac{\sqrt{91}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{91}}{2*-1}=\frac{0+2\sqrt{91}}{-2}
=\frac{2\sqrt{91}}{-2}
=\frac{\sqrt{91}}{-1}
$