19-1/x^2=0

Solution for 19-1/x^2=0 equation:

19-1/x^2=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


19*x^2-1=0

We add all the numbers together, and all the variables

19x^2-1=0

a = 19; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·19·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{19}}{2*19}=\frac{0-2\sqrt{19}}{38}
=-\frac{2\sqrt{19}}{38}
=-\frac{\sqrt{19}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{19}}{2*19}=\frac{0+2\sqrt{19}}{38}
=\frac{2\sqrt{19}}{38}
=\frac{\sqrt{19}}{19}
$