n^2=64/121

Solution for n^2=64/121 equation:

n^2=64/121

We move all terms to the left:

n^2-(64/121)=0

We add all the numbers together, and all the variables

n^2-(+64/121)=0

We get rid of parentheses

n^2-64/121=0

We multiply all the terms by the denominator


n^2*121-64=0

Wy multiply elements

121n^2-64=0

a = 121; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·121·(-64)
Δ = 30976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30976}=176$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-176}{2*121}=\frac{-176}{242}
=-8/11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+176}{2*121}=\frac{176}{242}
=8/11
$