x-3/X-12=9

Solution for x-3/X-12=9 equation:

x-3/x-12=9

We move all terms to the left:

x-3/x-12-(9)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-3/x-21=0

We multiply all the terms by the denominator


x*x-21*x-3=0

We add all the numbers together, and all the variables

-21x+x*x-3=0

Wy multiply elements

x^2-21x-3=0

a = 1; b = -21; c = -3;
Δ = b2-4ac
Δ = -212-4·1·(-3)
Δ = 453
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{453}}{2*1}=\frac{21-\sqrt{453}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{453}}{2*1}=\frac{21+\sqrt{453}}{2}
$