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1/3x-2=4x+9
We move all terms to the left:
1/3x-2-(4x+9)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
1/3x-4x-9-2=0
We multiply all the terms by the denominator
-4x*3x-9*3x-2*3x+1=0
Wy multiply elements
-12x^2-27x-6x+1=0
We add all the numbers together, and all the variables
-12x^2-33x+1=0
a = -12; b = -33; c = +1;
Δ = b2-4ac
Δ = -332-4·(-12)·1
Δ = 1137
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{1137}}{2*-12}=\frac{33-\sqrt{1137}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1137}}{2*-12}=\frac{33+\sqrt{1137}}{-24} $
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