-5x(x+1)=2x+8(-2x-4)

Solution for -5x(x+1)=2x+8(-2x-4) equation:

-5x(x+1)=2x+8(-2x-4)

We move all terms to the left:

-5x(x+1)-(2x+8(-2x-4))=0

We multiply parentheses

-5x^2-5x-(2x+8(-2x-4))=0


We calculate terms in parentheses: -(2x+8(-2x-4)), so:

2x+8(-2x-4)

We multiply parentheses

2x-16x-32

We add all the numbers together, and all the variables

-14x-32

Back to the equation:

-(-14x-32)


We get rid of parentheses

-5x^2-5x+14x+32=0

We add all the numbers together, and all the variables

-5x^2+9x+32=0

a = -5; b = 9; c = +32;
Δ = b2-4ac
Δ = 92-4·(-5)·32
Δ = 721
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{-(9)-\sqrt{721}}{2*-5}=\frac{-9-\sqrt{721}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{721}}{2*-5}=\frac{-9+\sqrt{721}}{-10}
$