X=4x-12/x-3

Solution for X=4x-12/x-3 equation:

X=4X-12/X-3

We move all terms to the left:

X-(4X-12/X-3)=0


Domain of the equation: X-3)!=0

X∈R


We get rid of parentheses

X-4X+12/X+3=0

We multiply all the terms by the denominator


X*X-4X*X+3*X+12=0

We add all the numbers together, and all the variables

3X+X*X-4X*X+12=0

Wy multiply elements

X^2-4X^2+3X+12=0

We add all the numbers together, and all the variables

-3X^2+3X+12=0

a = -3; b = 3; c = +12;
Δ = b2-4ac
Δ = 32-4·(-3)·12
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{17}}{2*-3}=\frac{-3-3\sqrt{17}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{17}}{2*-3}=\frac{-3+3\sqrt{17}}{-6}
$