3n(1/4)=161/2

Solution for 3n(1/4)=161/2 equation:

3n(1/4)=161/2

We move all terms to the left:

3n(1/4)-(161/2)=0

We add all the numbers together, and all the variables

3n(+1/4)-(+161/2)=0

We multiply parentheses

3n^2-(+161/2)=0

We get rid of parentheses

3n^2-161/2=0

We multiply all the terms by the denominator


3n^2*2-161=0

Wy multiply elements

6n^2-161=0

a = 6; b = 0; c = -161;
Δ = b2-4ac
Δ = 02-4·6·(-161)
Δ = 3864
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:

$\sqrt{\Delta}=\sqrt{3864}=\sqrt{4*966}=\sqrt{4}*\sqrt{966}=2\sqrt{966}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{966}}{2*6}=\frac{0-2\sqrt{966}}{12}
=-\frac{2\sqrt{966}}{12}
=-\frac{\sqrt{966}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{966}}{2*6}=\frac{0+2\sqrt{966}}{12}
=\frac{2\sqrt{966}}{12}
=\frac{\sqrt{966}}{6}
$