6n^2-66n+177=-3

Solution for 6n^2-66n+177=-3 equation:

6n^2-66n+177=-3

We move all terms to the left:

6n^2-66n+177-(-3)=0

We add all the numbers together, and all the variables

6n^2-66n+180=0

a = 6; b = -66; c = +180;
Δ = b2-4ac
Δ = -662-4·6·180
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6}{2*6}=\frac{60}{12}
=5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6}{2*6}=\frac{72}{12}
=6
$