23=71/(x^2)

Solution for 23=71/(x^2) equation:

23=71/(x^2)

We move all terms to the left:

23-(71/(x^2))=0


Domain of the equation: x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-71/x^2+23=0

We multiply all the terms by the denominator


23*x^2-71=0

We add all the numbers together, and all the variables

23x^2-71=0

a = 23; b = 0; c = -71;
Δ = b2-4ac
Δ = 02-4·23·(-71)
Δ = 6532
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:

$\sqrt{\Delta}=\sqrt{6532}=\sqrt{4*1633}=\sqrt{4}*\sqrt{1633}=2\sqrt{1633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1633}}{2*23}=\frac{0-2\sqrt{1633}}{46}
=-\frac{2\sqrt{1633}}{46}
=-\frac{\sqrt{1633}}{23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1633}}{2*23}=\frac{0+2\sqrt{1633}}{46}
=\frac{2\sqrt{1633}}{46}
=\frac{\sqrt{1633}}{23}
$