x-2/x-8=13

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}
$