x(x+2)+7(x+2)=0

Solution for x(x+2)+7(x+2)=0 equation:

x(x+2)+7(x+2)=0

We multiply parentheses

x^2+2x+7x+14=0

We add all the numbers together, and all the variables

x^2+9x+14=0

a = 1; b = 9; c = +14;
Δ = b2-4ac
Δ = 92-4·1·14
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5}{2*1}=\frac{-4}{2}
=-2
$