-1/3x-5=2x+9

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Solution for -1/3x-5=2x+9 equation:



-1/3x-5=2x+9
We move all terms to the left:
-1/3x-5-(2x+9)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We get rid of parentheses
-1/3x-2x-9-5=0
We multiply all the terms by the denominator
-2x*3x-9*3x-5*3x-1=0
Wy multiply elements
-6x^2-27x-15x-1=0
We add all the numbers together, and all the variables
-6x^2-42x-1=0
a = -6; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·(-6)·(-1)
Δ = 1740
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:
$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{435}}{2*-6}=\frac{42-2\sqrt{435}}{-12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{435}}{2*-6}=\frac{42+2\sqrt{435}}{-12} $

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