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

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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 $

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