1/3x+3=x-2

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



1/3x+3=x-2
We move all terms to the left:
1/3x+3-(x-2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We get rid of parentheses
1/3x-x+2+3=0
We multiply all the terms by the denominator
-x*3x+2*3x+3*3x+1=0
Wy multiply elements
-3x^2+6x+9x+1=0
We add all the numbers together, and all the variables
-3x^2+15x+1=0
a = -3; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-3)·1
Δ = 237
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{-(15)-\sqrt{237}}{2*-3}=\frac{-15-\sqrt{237}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{237}}{2*-3}=\frac{-15+\sqrt{237}}{-6} $

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