6n^2-3n-19=-2

Solution for 6n^2-3n-19=-2 equation:

6n^2-3n-19=-2

We move all terms to the left:

6n^2-3n-19-(-2)=0

We add all the numbers together, and all the variables

6n^2-3n-17=0

a = 6; b = -3; c = -17;
Δ = b2-4ac
Δ = -32-4·6·(-17)
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{417}}{2*6}=\frac{3-\sqrt{417}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{417}}{2*6}=\frac{3+\sqrt{417}}{12}
$