(X+1)(x-15)=16

Solution for (X+1)(x-15)=16 equation:

(X+1)(X-15)=16

We move all terms to the left:

(X+1)(X-15)-(16)=0

We multiply parentheses ..

(+X^2-15X+X-15)-16=0

We get rid of parentheses

X^2-15X+X-15-16=0

We add all the numbers together, and all the variables

X^2-14X-31=0

a = 1; b = -14; c = -31;
Δ = b2-4ac
Δ = -142-4·1·(-31)
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8\sqrt{5}}{2*1}=\frac{14-8\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8\sqrt{5}}{2*1}=\frac{14+8\sqrt{5}}{2}
$