2=x+7/x-12

Solution for 2=x+7/x-12 equation:

2=x+7/x-12

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

-x-7/x+12+2=0

We multiply all the terms by the denominator


-x*x+12*x+2*x-7=0

We add all the numbers together, and all the variables

14x-x*x-7=0

Wy multiply elements

-1x^2+14x-7=0

a = -1; b = 14; c = -7;
Δ = b2-4ac
Δ = 142-4·(-1)·(-7)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{42}}{2*-1}=\frac{-14-2\sqrt{42}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{42}}{2*-1}=\frac{-14+2\sqrt{42}}{-2}
$