12x^2-19=-2

Solution for 12x^2-19=-2 equation:

12x^2-19=-2

We move all terms to the left:

12x^2-19-(-2)=0

We add all the numbers together, and all the variables

12x^2-17=0

a = 12; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·12·(-17)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{51}}{2*12}=\frac{0-4\sqrt{51}}{24}
=-\frac{4\sqrt{51}}{24}
=-\frac{\sqrt{51}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{51}}{2*12}=\frac{0+4\sqrt{51}}{24}
=\frac{4\sqrt{51}}{24}
=\frac{\sqrt{51}}{6}
$