28=8/x^2

Solution for 28=8/x^2 equation:

28=8/x^2

We move all terms to the left:

28-(8/x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-8/x^2+28=0

We multiply all the terms by the denominator


28*x^2-8=0

We add all the numbers together, and all the variables

28x^2-8=0

a = 28; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·28·(-8)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*28}=\frac{0-8\sqrt{14}}{56}
=-\frac{8\sqrt{14}}{56}
=-\frac{\sqrt{14}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*28}=\frac{0+8\sqrt{14}}{56}
=\frac{8\sqrt{14}}{56}
=\frac{\sqrt{14}}{7}
$