3n^2-11n-45=-3

Solution for 3n^2-11n-45=-3 equation:

3n^2-11n-45=-3

We move all terms to the left:

3n^2-11n-45-(-3)=0

We add all the numbers together, and all the variables

3n^2-11n-42=0

a = 3; b = -11; c = -42;
Δ = b2-4ac
Δ = -112-4·3·(-42)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-25}{2*3}=\frac{-14}{6}
=-2+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+25}{2*3}=\frac{36}{6}
=6
$