n^2=64/49

Solution for n^2=64/49 equation:

n^2=64/49

We move all terms to the left:

n^2-(64/49)=0

We add all the numbers together, and all the variables

n^2-(+64/49)=0

We get rid of parentheses

n^2-64/49=0

We multiply all the terms by the denominator


n^2*49-64=0

Wy multiply elements

49n^2-64=0

a = 49; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·49·(-64)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-112}{2*49}=\frac{-112}{98}
=-1+1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+112}{2*49}=\frac{112}{98}
=1+1/7
$