7/x^2=400

Solution for 7/x^2=400 equation:

7/x^2=400

We move all terms to the left:

7/x^2-(400)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-400*x^2+7=0

We add all the numbers together, and all the variables

-400x^2+7=0

a = -400; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-400)·7
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{7}}{2*-400}=\frac{0-40\sqrt{7}}{-800}
=-\frac{40\sqrt{7}}{-800}
=-\frac{\sqrt{7}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{7}}{2*-400}=\frac{0+40\sqrt{7}}{-800}
=\frac{40\sqrt{7}}{-800}
=\frac{\sqrt{7}}{-20}
$