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^2-16x-17

Back to the equation:

-(x^2-16x-17)


We get rid of parentheses

-x^2+16x+17+17=0

We add all the numbers together, and all the variables

-1x^2+16x+34=0

a = -1; b = 16; c = +34;
Δ = b2-4ac
Δ = 162-4·(-1)·34
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-14\sqrt{2}}{2*-1}=\frac{-16-14\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+14\sqrt{2}}{2*-1}=\frac{-16+14\sqrt{2}}{-2}
$