x+7/x-7=15

Solution for x+7/x-7=15 equation:

x+7/x-7=15

We move all terms to the left:

x+7/x-7-(15)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+7/x-22=0

We multiply all the terms by the denominator


x*x-22*x+7=0

We add all the numbers together, and all the variables

-22x+x*x+7=0

Wy multiply elements

x^2-22x+7=0

a = 1; b = -22; c = +7;
Δ = b2-4ac
Δ = -222-4·1·7
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{114}}{2*1}=\frac{22-2\sqrt{114}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{114}}{2*1}=\frac{22+2\sqrt{114}}{2}
$