144=4(3a)^2

Solution for 144=4(3a)^2 equation:

144=4(3a)^2

We move all terms to the left:

144-(4(3a)^2)=0

determiningTheFunctionDomain
-43a^2+144=0

a = -43; b = 0; c = +144;
Δ = b2-4ac
Δ = 02-4·(-43)·144
Δ = 24768
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:

$\sqrt{\Delta}=\sqrt{24768}=\sqrt{576*43}=\sqrt{576}*\sqrt{43}=24\sqrt{43}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{43}}{2*-43}=\frac{0-24\sqrt{43}}{-86}
=-\frac{24\sqrt{43}}{-86}
=-\frac{12\sqrt{43}}{-43}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{43}}{2*-43}=\frac{0+24\sqrt{43}}{-86}
=\frac{24\sqrt{43}}{-86}
=\frac{12\sqrt{43}}{-43}
$