(406/(x^2))=4

Solution for (406/(x^2))=4 equation:

(406/(x^2))=4

We move all terms to the left:

(406/(x^2))-(4)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

406/x^2-4=0

We multiply all the terms by the denominator


-4*x^2+406=0

We add all the numbers together, and all the variables

-4x^2+406=0

a = -4; b = 0; c = +406;
Δ = b2-4ac
Δ = 02-4·(-4)·406
Δ = 6496
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:

$\sqrt{\Delta}=\sqrt{6496}=\sqrt{16*406}=\sqrt{16}*\sqrt{406}=4\sqrt{406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{406}}{2*-4}=\frac{0-4\sqrt{406}}{-8}
=-\frac{4\sqrt{406}}{-8}
=-\frac{\sqrt{406}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{406}}{2*-4}=\frac{0+4\sqrt{406}}{-8}
=\frac{4\sqrt{406}}{-8}
=\frac{\sqrt{406}}{-2}
$