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

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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 $

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