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1/3x-2=x-6

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



1/3x-2=x-6
We move all terms to the left:
1/3x-2-(x-6)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We get rid of parentheses
1/3x-x+6-2=0
We multiply all the terms by the denominator
-x*3x+6*3x-2*3x+1=0
Wy multiply elements
-3x^2+18x-6x+1=0
We add all the numbers together, and all the variables
-3x^2+12x+1=0
a = -3; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-3)·1
Δ = 156
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{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{39}}{2*-3}=\frac{-12-2\sqrt{39}}{-6}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{39}}{2*-3}=\frac{-12+2\sqrt{39}}{-6}

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