1/x^2x=7

Solution for 1/x^2x=7 equation:

1/x^2x=7

We move all terms to the left:

1/x^2x-(7)=0


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

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-7*x^2x+1=0

Wy multiply elements

-7x^2+1=0

a = -7; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-7)·1
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*-7}=\frac{0-2\sqrt{7}}{-14}
=-\frac{2\sqrt{7}}{-14}
=-\frac{\sqrt{7}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*-7}=\frac{0+2\sqrt{7}}{-14}
=\frac{2\sqrt{7}}{-14}
=\frac{\sqrt{7}}{-7}
$