2166=6x^2

Solution for 2166=6x^2 equation:

2166=6x^2

We move all terms to the left:

2166-(6x^2)=0

a = -6; b = 0; c = +2166;
Δ = b2-4ac
Δ = 02-4·(-6)·2166
Δ = 51984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51984}=228$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-228}{2*-6}=\frac{-228}{-12}
=+19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+228}{2*-6}=\frac{228}{-12}
=-19
$