5x-2/x-4=2

Solution for 5x-2/x-4=2 equation:

5x-2/x-4=2

We move all terms to the left:

5x-2/x-4-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-2/x-6=0

We multiply all the terms by the denominator


5x*x-6*x-2=0

We add all the numbers together, and all the variables

-6x+5x*x-2=0

Wy multiply elements

5x^2-6x-2=0

a = 5; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·5·(-2)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*5}=\frac{6-2\sqrt{19}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*5}=\frac{6+2\sqrt{19}}{10}
$