x+5/x-7=12

Solution for x+5/x-7=12 equation:

x+5/x-7=12

We move all terms to the left:

x+5/x-7-(12)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+5/x-19=0

We multiply all the terms by the denominator


x*x-19*x+5=0

We add all the numbers together, and all the variables

-19x+x*x+5=0

Wy multiply elements

x^2-19x+5=0

a = 1; b = -19; c = +5;
Δ = b2-4ac
Δ = -192-4·1·5
Δ = 341
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{-(-19)-\sqrt{341}}{2*1}=\frac{19-\sqrt{341}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{341}}{2*1}=\frac{19+\sqrt{341}}{2}
$