x+7/x-7=5

Solution for x+7/x-7=5 equation:

x+7/x-7=5

We move all terms to the left:

x+7/x-7-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+7/x-12=0

We multiply all the terms by the denominator


x*x-12*x+7=0

We add all the numbers together, and all the variables

-12x+x*x+7=0

Wy multiply elements

x^2-12x+7=0

a = 1; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·1·7
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{29}}{2*1}=\frac{12-2\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{29}}{2*1}=\frac{12+2\sqrt{29}}{2}
$