8=5/x^2

Solution for 8=5/x^2 equation:

8=5/x^2

We move all terms to the left:

8-(5/x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-5/x^2+8=0

We multiply all the terms by the denominator


8*x^2-5=0

We add all the numbers together, and all the variables

8x^2-5=0

a = 8; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·8·(-5)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*8}=\frac{0-4\sqrt{10}}{16}
=-\frac{4\sqrt{10}}{16}
=-\frac{\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*8}=\frac{0+4\sqrt{10}}{16}
=\frac{4\sqrt{10}}{16}
=\frac{\sqrt{10}}{4}
$