1/x+1/x-7=x-6/x-7

Solution for 1/x+1/x-7=x-6/x-7 equation:

1/x+1/x-7=x-6/x-7

We move all terms to the left:

1/x+1/x-7-(x-6/x-7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-7)!=0

x∈R


We get rid of parentheses

1/x+1/x-x+6/x+7-7=0

We multiply all the terms by the denominator


-x*x+7*x-7*x+1+1+6=0

We add all the numbers together, and all the variables

-x*x+8=0

Wy multiply elements

-1x^2+8=0

a = -1; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-1)·8
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{-(0)-4\sqrt{2}}{2*-1}=\frac{0-4\sqrt{2}}{-2}
=-\frac{4\sqrt{2}}{-2}
=-\frac{2\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*-1}=\frac{0+4\sqrt{2}}{-2}
=\frac{4\sqrt{2}}{-2}
=\frac{2\sqrt{2}}{-1}
$