3n^2-n-12=0

Solution for 3n^2-n-12=0 equation:

3n^2-n-12=0

We add all the numbers together, and all the variables

3n^2-1n-12=0

a = 3; b = -1; c = -12;
Δ = b2-4ac
Δ = -12-4·3·(-12)
Δ = 145
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{-(-1)-\sqrt{145}}{2*3}=\frac{1-\sqrt{145}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*3}=\frac{1+\sqrt{145}}{6}
$