483=12x^2

Solution for 483=12x^2 equation:

483=12x^2

We move all terms to the left:

483-(12x^2)=0

a = -12; b = 0; c = +483;
Δ = b2-4ac
Δ = 02-4·(-12)·483
Δ = 23184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{23184}=\sqrt{144*161}=\sqrt{144}*\sqrt{161}=12\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{161}}{2*-12}=\frac{0-12\sqrt{161}}{-24}
=-\frac{12\sqrt{161}}{-24}
=-\frac{\sqrt{161}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{161}}{2*-12}=\frac{0+12\sqrt{161}}{-24}
=\frac{12\sqrt{161}}{-24}
=\frac{\sqrt{161}}{-2}
$