3n^2-21n+18=0

Solution for 3n^2-21n+18=0 equation:

3n^2-21n+18=0

a = 3; b = -21; c = +18;
Δ = b2-4ac
Δ = -212-4·3·18
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-15}{2*3}=\frac{6}{6}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+15}{2*3}=\frac{36}{6}
=6
$