5/x2+1=11

Solution for 5/x2+1=11 equation:

5/x2+1=11

We move all terms to the left:

5/x2+1-(11)=0


Domain of the equation: x2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

5/x2-10=0

We multiply all the terms by the denominator


-10*x2+5=0

We add all the numbers together, and all the variables

-10x^2+5=0

a = -10; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-10)·5
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*-10}=\frac{0-10\sqrt{2}}{-20}
=-\frac{10\sqrt{2}}{-20}
=-\frac{\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*-10}=\frac{0+10\sqrt{2}}{-20}
=\frac{10\sqrt{2}}{-20}
=\frac{\sqrt{2}}{-2}
$