50/x^2-25=0

Solution for 50/x^2-25=0 equation:

50/x^2-25=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


-25*x^2+50=0

We add all the numbers together, and all the variables

-25x^2+50=0

a = -25; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-25)·50
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{2}}{2*-25}=\frac{0-50\sqrt{2}}{-50}
=-\frac{50\sqrt{2}}{-50}
=-\frac{\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{2}}{2*-25}=\frac{0+50\sqrt{2}}{-50}
=\frac{50\sqrt{2}}{-50}
=\frac{\sqrt{2}}{-1}
$