9=x-4/x-12

Solution for 9=x-4/x-12 equation:

9=x-4/x-12

We move all terms to the left:

9-(x-4/x-12)=0


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

x∈R


We get rid of parentheses

-x+4/x+12+9=0

We multiply all the terms by the denominator


-x*x+12*x+9*x+4=0

We add all the numbers together, and all the variables

21x-x*x+4=0

Wy multiply elements

-1x^2+21x+4=0

a = -1; b = 21; c = +4;
Δ = b2-4ac
Δ = 212-4·(-1)·4
Δ = 457
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{-(21)-\sqrt{457}}{2*-1}=\frac{-21-\sqrt{457}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{457}}{2*-1}=\frac{-21+\sqrt{457}}{-2}
$