x-2/x-8=13

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Solution for x-2/x-8=13 equation:



x-2/x-8=13
We move all terms to the left:
x-2/x-8-(13)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
x-2/x-21=0
We multiply all the terms by the denominator
x*x-21*x-2=0
We add all the numbers together, and all the variables
-21x+x*x-2=0
Wy multiply elements
x^2-21x-2=0
a = 1; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·1·(-2)
Δ = 449
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{-(-21)-\sqrt{449}}{2*1}=\frac{21-\sqrt{449}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{449}}{2*1}=\frac{21+\sqrt{449}}{2} $

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