n^2=49/81

Solution for n^2=49/81 equation:

n^2=49/81

We move all terms to the left:

n^2-(49/81)=0

We add all the numbers together, and all the variables

n^2-(+49/81)=0

We get rid of parentheses

n^2-49/81=0

We multiply all the terms by the denominator


n^2*81-49=0

Wy multiply elements

81n^2-49=0

a = 81; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·81·(-49)
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-126}{2*81}=\frac{-126}{162}
=-7/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+126}{2*81}=\frac{126}{162}
=7/9
$