3/4*n=54

Solution for 3/4*n=54 equation:

3/4*n=54

We move all terms to the left:

3/4*n-(54)=0


Domain of the equation: 4*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-54*4*n+3=0

Wy multiply elements

-216n*n+3=0

Wy multiply elements

-216n^2+3=0

a = -216; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-216)·3
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*-216}=\frac{0-36\sqrt{2}}{-432}
=-\frac{36\sqrt{2}}{-432}
=-\frac{\sqrt{2}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*-216}=\frac{0+36\sqrt{2}}{-432}
=\frac{36\sqrt{2}}{-432}
=\frac{\sqrt{2}}{-12}
$