-5x(x+4)=12-40-7x

Solution for -5x(x+4)=12-40-7x equation:

-5x(x+4)=12-40-7x

We move all terms to the left:

-5x(x+4)-(12-40-7x)=0

We add all the numbers together, and all the variables

-5x(x+4)-(-7x-28)=0

We multiply parentheses

-5x^2-20x-(-7x-28)=0

We get rid of parentheses

-5x^2-20x+7x+28=0

We add all the numbers together, and all the variables

-5x^2-13x+28=0

a = -5; b = -13; c = +28;
Δ = b2-4ac
Δ = -132-4·(-5)·28
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-27}{2*-5}=\frac{-14}{-10}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+27}{2*-5}=\frac{40}{-10}
=-4
$