x(x+7)=-2

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

x(x+7)=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(x+7)+2=0

We multiply parentheses

x^2+7x+2=0

a = 1; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·1·2
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{41}}{2*1}=\frac{-7-\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{41}}{2*1}=\frac{-7+\sqrt{41}}{2}
$