x^2-6x-7=x

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Solution for x^2-6x-7=x equation:



x^2-6x-7=x
We move all terms to the left:
x^2-6x-7-(x)=0
We add all the numbers together, and all the variables
x^2-7x-7=0
a = 1; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·1·(-7)
Δ = 77
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{77}}{2*1}=\frac{7-\sqrt{77}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{77}}{2*1}=\frac{7+\sqrt{77}}{2} $

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