3x-2/x-10=2x-3/x-6

Solution for 3x-2/x-10=2x-3/x-6 equation:

3x-2/x-10=2x-3/x-6

We move all terms to the left:

3x-2/x-10-(2x-3/x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-6)!=0

x∈R


We get rid of parentheses

3x-2/x-2x+3/x+6-10=0

We multiply all the terms by the denominator


3x*x-2x*x+6*x-10*x-2+3=0

We add all the numbers together, and all the variables

-4x+3x*x-2x*x+1=0

Wy multiply elements

3x^2-2x^2-4x+1=0

We add all the numbers together, and all the variables

x^2-4x+1=0

a = 1; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·1·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{3}}{2*1}=\frac{4-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{3}}{2*1}=\frac{4+2\sqrt{3}}{2}
$