4/9*n=18

Solution for 4/9*n=18 equation:

4/9*n=18

We move all terms to the left:

4/9*n-(18)=0


Domain of the equation: 9*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-18*9*n+4=0

Wy multiply elements

-162n*n+4=0

Wy multiply elements

-162n^2+4=0

a = -162; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-162)·4
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*-162}=\frac{0-36\sqrt{2}}{-324}
=-\frac{36\sqrt{2}}{-324}
=-\frac{\sqrt{2}}{-9}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*-162}=\frac{0+36\sqrt{2}}{-324}
=\frac{36\sqrt{2}}{-324}
=\frac{\sqrt{2}}{-9}
$