3n(n=11)

Solution for 3n(n=11) equation:

3n(n=11)

We move all terms to the left:

3n(n-(11))=0

We multiply parentheses

3n^2-33n=0

a = 3; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·3·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*3}=\frac{0}{6}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*3}=\frac{66}{6}
=11
$