2x+17=(x+5)(x+1)

Solution for 2x+17=(x+5)(x+1) equation:

2x+17=(x+5)(x+1)

We move all terms to the left:

2x+17-((x+5)(x+1))=0

We multiply parentheses ..

-((+x^2+x+5x+5))+2x+17=0


We calculate terms in parentheses: -((+x^2+x+5x+5)), so:

(+x^2+x+5x+5)

We get rid of parentheses

x^2+x+5x+5

We add all the numbers together, and all the variables

x^2+6x+5

Back to the equation:

-(x^2+6x+5)


We add all the numbers together, and all the variables

2x-(x^2+6x+5)+17=0

We get rid of parentheses

-x^2+2x-6x-5+17=0

We add all the numbers together, and all the variables

-1x^2-4x+12=0

a = -1; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-1}=\frac{12}{-2}
=-6
$