3n^2-36n+105=O

Solution for 3n^2-36n+105=O equation:

3n^2-36n+105=

We move all terms to the left:

3n^2-36n+105-()=0

We add all the numbers together, and all the variables

3n^2-36n=0

a = 3; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·3·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*3}=\frac{0}{6}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*3}=\frac{72}{6}
=12
$