Y9/x=x

Solution for Y9/x=x equation:

9/Y=Y

We move all terms to the left:

9/Y-(Y)=0


Domain of the equation: Y!=0

Y∈R


We add all the numbers together, and all the variables

-1Y+9/Y=0

We multiply all the terms by the denominator


-1Y*Y+9=0

Wy multiply elements

-1Y^2+9=0

a = -1; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-1)·9
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-1}=\frac{-6}{-2}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-1}=\frac{6}{-2}
=-3
$