x-7/x-6=2x-11/x-2

Solution for x-7/x-6=2x-11/x-2 equation:

x-7/x-6=2x-11/x-2

We move all terms to the left:

x-7/x-6-(2x-11/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-7/x-2x+11/x+2-6=0

We multiply all the terms by the denominator


x*x-2x*x+2*x-6*x-7+11=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -1; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-1)·4
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*-1}=\frac{4-4\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*-1}=\frac{4+4\sqrt{2}}{-2}
$