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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((5x+5)(-2x+8)), so:

(5x+5)(-2x+8)

We multiply parentheses ..

(-10x^2+40x-10x+40)

We get rid of parentheses

-10x^2+40x-10x+40

We add all the numbers together, and all the variables

-10x^2+30x+40

Back to the equation:

-(-10x^2+30x+40)


We get rid of parentheses

-2x^2+10x^2-2x+8x-30x+8-40=0

We add all the numbers together, and all the variables

8x^2-24x-32=0

a = 8; b = -24; c = -32;
Δ = b2-4ac
Δ = -242-4·8·(-32)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-40}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+40}{2*8}=\frac{64}{16}
=4
$