X+4=6x-12/x-2=3x+12

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Solution for X+4=6x-12/x-2=3x+12 equation:



X+4=6X-12/X-2=3X+12
We move all terms to the left:
X+4-(6X-12/X-2)=0
Domain of the equation: X-2)!=0
X∈R
We get rid of parentheses
X-6X+12/X+2+4=0
We multiply all the terms by the denominator
X*X-6X*X+2*X+4*X+12=0
We add all the numbers together, and all the variables
6X+X*X-6X*X+12=0
Wy multiply elements
X^2-6X^2+6X+12=0
We add all the numbers together, and all the variables
-5X^2+6X+12=0
a = -5; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-5)·12
Δ = 276
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:
$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*-5}=\frac{-6-2\sqrt{69}}{-10} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*-5}=\frac{-6+2\sqrt{69}}{-10} $

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