-3x2-2=-46

Solution for -3x2-2=-46 equation:

-3x^2-2=-46

We move all terms to the left:

-3x^2-2-(-46)=0

We add all the numbers together, and all the variables

-3x^2+44=0

a = -3; b = 0; c = +44;
Δ = b2-4ac
Δ = 02-4·(-3)·44
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*-3}=\frac{0-4\sqrt{33}}{-6}
=-\frac{4\sqrt{33}}{-6}
=-\frac{2\sqrt{33}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*-3}=\frac{0+4\sqrt{33}}{-6}
=\frac{4\sqrt{33}}{-6}
=\frac{2\sqrt{33}}{-3}
$