X(x+2)+17(x+2)=0

Solution for X(x+2)+17(x+2)=0 equation:

X(X+2)+17(X+2)=0

We multiply parentheses

X^2+2X+17X+34=0

We add all the numbers together, and all the variables

X^2+19X+34=0

a = 1; b = 19; c = +34;
Δ = b2-4ac
Δ = 192-4·1·34
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-15}{2*1}=\frac{-34}{2}
=-17
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+15}{2*1}=\frac{-4}{2}
=-2
$