(n+3)(n-2)=54

Solution for (n+3)(n-2)=54 equation:

(n+3)(n-2)=54

We move all terms to the left:

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

We multiply parentheses ..

(+n^2-2n+3n-6)-54=0

We get rid of parentheses

n^2-2n+3n-6-54=0

We add all the numbers together, and all the variables

n^2+n-60=0

a = 1; b = 1; c = -60;
Δ = b2-4ac
Δ = 12-4·1·(-60)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{241}}{2*1}=\frac{-1-\sqrt{241}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{241}}{2*1}=\frac{-1+\sqrt{241}}{2}
$