(n-1)(n+6)=(n+5)

Solution for (n-1)(n+6)=(n+5) equation:

(n-1)(n+6)=(n+5)

We move all terms to the left:

(n-1)(n+6)-((n+5))=0

We multiply parentheses ..

(+n^2+6n-1n-6)-((n+5))=0


We calculate terms in parentheses: -((n+5)), so:

(n+5)

We get rid of parentheses

n+5

Back to the equation:

-(n+5)


We get rid of parentheses

n^2+6n-1n-n-6-5=0

We add all the numbers together, and all the variables

n^2+4n-11=0

a = 1; b = 4; c = -11;
Δ = b2-4ac
Δ = 42-4·1·(-11)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{15}}{2*1}=\frac{-4-2\sqrt{15}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{15}}{2*1}=\frac{-4+2\sqrt{15}}{2}
$