17=(x+1)(x+17)

Solution for 17=(x+1)(x+17) equation:

17=(x+1)(x+17)

We move all terms to the left:

17-((x+1)(x+17))=0

We multiply parentheses ..

-((+x^2+17x+x+17))+17=0


We calculate terms in parentheses: -((+x^2+17x+x+17)), so:

(+x^2+17x+x+17)

We get rid of parentheses

x^2+17x+x+17

We add all the numbers together, and all the variables

x^2+18x+17

Back to the equation:

-(x^2+18x+17)


We get rid of parentheses

-x^2-18x-17+17=0

We add all the numbers together, and all the variables

-1x^2-18x=0

a = -1; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-1)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-1}=\frac{36}{-2}
=-18
$