12x^2+1=19

Solution for 12x^2+1=19 equation:

12x^2+1=19

We move all terms to the left:

12x^2+1-(19)=0

We add all the numbers together, and all the variables

12x^2-18=0

a = 12; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·12·(-18)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*12}=\frac{0-12\sqrt{6}}{24}
=-\frac{12\sqrt{6}}{24}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*12}=\frac{0+12\sqrt{6}}{24}
=\frac{12\sqrt{6}}{24}
=\frac{\sqrt{6}}{2}
$