3x^2+2-10^2=66

Solution for 3x^2+2-10^2=66 equation:

3x^2+2-10^2=66

We move all terms to the left:

3x^2+2-10^2-(66)=0

determiningTheFunctionDomain
3x^2+2-66-10^2=0

We add all the numbers together, and all the variables

3x^2-164=0

a = 3; b = 0; c = -164;
Δ = b2-4ac
Δ = 02-4·3·(-164)
Δ = 1968
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:

$\sqrt{\Delta}=\sqrt{1968}=\sqrt{16*123}=\sqrt{16}*\sqrt{123}=4\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{123}}{2*3}=\frac{0-4\sqrt{123}}{6}
=-\frac{4\sqrt{123}}{6}
=-\frac{2\sqrt{123}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{123}}{2*3}=\frac{0+4\sqrt{123}}{6}
=\frac{4\sqrt{123}}{6}
=\frac{2\sqrt{123}}{3}
$