12n^2-3n=2

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

12n^2-3n=2

We move all terms to the left:

12n^2-3n-(2)=0

a = 12; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·12·(-2)
Δ = 105
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{105}}{2*12}=\frac{3-\sqrt{105}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*12}=\frac{3+\sqrt{105}}{24}
$