1/2n^2=50

Solution for 1/2n^2=50 equation:

1/2n^2=50

We move all terms to the left:

1/2n^2-(50)=0


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

n^2!=0/2

n^2!=√0

n!=0

n∈R


We multiply all the terms by the denominator


-50*2n^2+1=0

Wy multiply elements

-100n^2+1=0

a = -100; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-100)·1
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-100}=\frac{-20}{-200}
=1/10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-100}=\frac{20}{-200}
=-1/10
$