-2x+5=-1/3x-6

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Solution for -2x+5=-1/3x-6 equation:



-2x+5=-1/3x-6
We move all terms to the left:
-2x+5-(-1/3x-6)=0
Domain of the equation: 3x-6)!=0
x∈R
We get rid of parentheses
-2x+1/3x+6+5=0
We multiply all the terms by the denominator
-2x*3x+6*3x+5*3x+1=0
Wy multiply elements
-6x^2+18x+15x+1=0
We add all the numbers together, and all the variables
-6x^2+33x+1=0
a = -6; b = 33; c = +1;
Δ = b2-4ac
Δ = 332-4·(-6)·1
Δ = 1113
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{-(33)-\sqrt{1113}}{2*-6}=\frac{-33-\sqrt{1113}}{-12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1113}}{2*-6}=\frac{-33+\sqrt{1113}}{-12} $

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