3n^2-n+10=54

Solution for 3n^2-n+10=54 equation:

3n^2-n+10=54

We move all terms to the left:

3n^2-n+10-(54)=0

We add all the numbers together, and all the variables

3n^2-1n-44=0

a = 3; b = -1; c = -44;
Δ = b2-4ac
Δ = -12-4·3·(-44)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-23}{2*3}=\frac{-22}{6}
=-3+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+23}{2*3}=\frac{24}{6}
=4
$