n^2=3/25

Solution for n^2=3/25 equation:

n^2=3/25

We move all terms to the left:

n^2-(3/25)=0

We add all the numbers together, and all the variables

n^2-(+3/25)=0

We get rid of parentheses

n^2-3/25=0

We multiply all the terms by the denominator


n^2*25-3=0

Wy multiply elements

25n^2-3=0

a = 25; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·25·(-3)
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*25}=\frac{0-10\sqrt{3}}{50}
=-\frac{10\sqrt{3}}{50}
=-\frac{\sqrt{3}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*25}=\frac{0+10\sqrt{3}}{50}
=\frac{10\sqrt{3}}{50}
=\frac{\sqrt{3}}{5}
$