18*6=n*n

Solution for 18*6=n*n equation:

18*6=n*n

We move all terms to the left:

18*6-(n*n)=0

We add all the numbers together, and all the variables

-(+n*n)+18*6=0

We add all the numbers together, and all the variables

-(+n*n)+108=0

We get rid of parentheses

-n*n+108=0

Wy multiply elements

-1n^2+108=0

a = -1; b = 0; c = +108;
Δ = b2-4ac
Δ = 02-4·(-1)·108
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-1}=\frac{0-12\sqrt{3}}{-2}
=-\frac{12\sqrt{3}}{-2}
=-\frac{6\sqrt{3}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-1}=\frac{0+12\sqrt{3}}{-2}
=\frac{12\sqrt{3}}{-2}
=\frac{6\sqrt{3}}{-1}
$