6n^2+21n=12

Solution for 6n^2+21n=12 equation:

6n^2+21n=12

We move all terms to the left:

6n^2+21n-(12)=0

a = 6; b = 21; c = -12;
Δ = b2-4ac
Δ = 212-4·6·(-12)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*6}=\frac{-48}{12}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*6}=\frac{6}{12}
=1/2
$