x/x-6=x-8/x-11

Solution for x/x-6=x-8/x-11 equation:

x/x-6=x-8/x-11

We move all terms to the left:

x/x-6-(x-8/x-11)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-11)!=0

x∈R


We get rid of parentheses

x/x-x+8/x+11-6=0

Fractions to decimals

8/x-x+11-6+1=0

We multiply all the terms by the denominator


-x*x+11*x-6*x+1*x+8=0

We add all the numbers together, and all the variables

6x-x*x+8=0

Wy multiply elements

-1x^2+6x+8=0

a = -1; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-1)·8
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*-1}=\frac{-6-2\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*-1}=\frac{-6+2\sqrt{17}}{-2}
$