(x-8)(x+1)=-20

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Solution for (x-8)(x+1)=-20 equation:



(x-8)(x+1)=-20
We move all terms to the left:
(x-8)(x+1)-(-20)=0
We add all the numbers together, and all the variables
(x-8)(x+1)+20=0
We multiply parentheses ..
(+x^2+x-8x-8)+20=0
We get rid of parentheses
x^2+x-8x-8+20=0
We add all the numbers together, and all the variables
x^2-7x+12=0
a = 1; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·1·12
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*1}=\frac{6}{2} =3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*1}=\frac{8}{2} =4 $

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