-7x(x+2)=x+2

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Solution for -7x(x+2)=x+2 equation:



-7x(x+2)=x+2
We move all terms to the left:
-7x(x+2)-(x+2)=0
We multiply parentheses
-7x^2-14x-(x+2)=0
We get rid of parentheses
-7x^2-14x-x-2=0
We add all the numbers together, and all the variables
-7x^2-15x-2=0
a = -7; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·(-7)·(-2)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-13}{2*-7}=\frac{2}{-14} =-1/7 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+13}{2*-7}=\frac{28}{-14} =-2 $

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