x-15/15=2x-12/x+12

Solution for x-15/15=2x-12/x+12 equation:

x-15/15=2x-12/x+12

We move all terms to the left:

x-15/15-(2x-12/x+12)=0


Domain of the equation: x+12)!=0

x∈R


We add all the numbers together, and all the variables

x-(2x-12/x+12)-1=0

We get rid of parentheses

x-2x+12/x-12-1=0

We multiply all the terms by the denominator


x*x-2x*x-12*x-1*x+12=0

We add all the numbers together, and all the variables

-13x+x*x-2x*x+12=0

Wy multiply elements

x^2-2x^2-13x+12=0

We add all the numbers together, and all the variables

-1x^2-13x+12=0

a = -1; b = -13; c = +12;
Δ = b2-4ac
Δ = -132-4·(-1)·12
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{217}}{2*-1}=\frac{13-\sqrt{217}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{217}}{2*-1}=\frac{13+\sqrt{217}}{-2}
$