1/x+1/x-6=X-5/x-6

Solution for 1/x+1/x-6=X-5/x-6 equation:

1/x+1/x-6=x-5/x-6

We move all terms to the left:

1/x+1/x-6-(x-5/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

1/x+1/x-x+5/x+6-6=0

We multiply all the terms by the denominator


-x*x+6*x-6*x+1+1+5=0

We add all the numbers together, and all the variables

-x*x+7=0

Wy multiply elements

-1x^2+7=0

a = -1; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-1)·7
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*-1}=\frac{0-2\sqrt{7}}{-2}
=-\frac{2\sqrt{7}}{-2}
=-\frac{\sqrt{7}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*-1}=\frac{0+2\sqrt{7}}{-2}
=\frac{2\sqrt{7}}{-2}
=\frac{\sqrt{7}}{-1}
$