2x-20/x-20=6

Solution for 2x-20/x-20=6 equation:

2x-20/x-20=6

We move all terms to the left:

2x-20/x-20-(6)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-20/x-26=0

We multiply all the terms by the denominator


2x*x-26*x-20=0

We add all the numbers together, and all the variables

-26x+2x*x-20=0

Wy multiply elements

2x^2-26x-20=0

a = 2; b = -26; c = -20;
Δ = b2-4ac
Δ = -262-4·2·(-20)
Δ = 836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{209}}{2*2}=\frac{26-2\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{209}}{2*2}=\frac{26+2\sqrt{209}}{4}
$