(18a)^2-9-(2*6)3=36

Solution for (18a)^2-9-(2*6)3=36 equation:

(18a)^2-9-(2*6)3=36

We move all terms to the left:

(18a)^2-9-(2*6)3-(36)=0

determiningTheFunctionDomain
18a^2-9-36-(2*6)3=0

We add all the numbers together, and all the variables

18a^2-9-36-123=0

We add all the numbers together, and all the variables

18a^2-168=0

a = 18; b = 0; c = -168;
Δ = b2-4ac
Δ = 02-4·18·(-168)
Δ = 12096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{21}}{2*18}=\frac{0-24\sqrt{21}}{36}
=-\frac{24\sqrt{21}}{36}
=-\frac{2\sqrt{21}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{21}}{2*18}=\frac{0+24\sqrt{21}}{36}
=\frac{24\sqrt{21}}{36}
=\frac{2\sqrt{21}}{3}
$