7x=-x^2-4x

Solution for 7x=-x^2-4x equation:

7x=-x^2-4x

We move all terms to the left:

7x-(-x^2-4x)=0

We get rid of parentheses

x^2+4x+7x=0

We add all the numbers together, and all the variables

x^2+11x=0

a = 1; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·1·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*1}=\frac{0}{2}
=0
$