(x+8)(3x+5)=-(x+8)(x-1)

Solution for (x+8)(3x+5)=-(x+8)(x-1) equation:

(x+8)(3x+5)=-(x+8)(x-1)

We move all terms to the left:

(x+8)(3x+5)-(-(x+8)(x-1))=0

We multiply parentheses ..

(+3x^2+5x+24x+40)-(-(x+8)(x-1))=0


We calculate terms in parentheses: -(-(x+8)(x-1)), so:

-(x+8)(x-1)

We multiply parentheses ..

-(+x^2-1x+8x-8)

We get rid of parentheses

-x^2+1x-8x+8

We add all the numbers together, and all the variables

-1x^2-7x+8

Back to the equation:

-(-1x^2-7x+8)


We get rid of parentheses

3x^2+1x^2+5x+24x+7x+40-8=0

We add all the numbers together, and all the variables

4x^2+36x+32=0

a = 4; b = 36; c = +32;
Δ = b2-4ac
Δ = 362-4·4·32
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-28}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+28}{2*4}=\frac{-8}{8}
=-1
$