x-10/x-4=3x/x-2

Solution for x-10/x-4=3x/x-2 equation:

x-10/x-4=3x/x-2

We move all terms to the left:

x-10/x-4-(3x/x-2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

x-10/x-3x/x+2-4=0

We multiply all the terms by the denominator


x*x-3x+2*x-4*x-10=0

We add all the numbers together, and all the variables

-5x+x*x-10=0

Wy multiply elements

x^2-5x-10=0

a = 1; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·1·(-10)
Δ = 65
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{-(-5)-\sqrt{65}}{2*1}=\frac{5-\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*1}=\frac{5+\sqrt{65}}{2}
$