144n^2-3=-2

Solution for 144n^2-3=-2 equation:

144n^2-3=-2

We move all terms to the left:

144n^2-3-(-2)=0

We add all the numbers together, and all the variables

144n^2-1=0

a = 144; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·144·(-1)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*144}=\frac{-24}{288}
=-1/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*144}=\frac{24}{288}
=1/12
$