x(x+6)=-7x

Solution for x(x+6)=-7x equation:

x(x+6)=-7x

We move all terms to the left:

x(x+6)-(-7x)=0

We multiply parentheses

x^2+6x-(-7x)=0

We get rid of parentheses

x^2+6x+7x=0

We add all the numbers together, and all the variables

x^2+13x=0

a = 1; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·1·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*1}=\frac{0}{2}
=0
$