3n(n-1)=21

Solution for 3n(n-1)=21 equation:

3n(n-1)=21

We move all terms to the left:

3n(n-1)-(21)=0

We multiply parentheses

3n^2-3n-21=0

a = 3; b = -3; c = -21;
Δ = b2-4ac
Δ = -32-4·3·(-21)
Δ = 261
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{29}}{2*3}=\frac{3-3\sqrt{29}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{29}}{2*3}=\frac{3+3\sqrt{29}}{6}
$