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1/3x+3=4x-2
We move all terms to the left:
1/3x+3-(4x-2)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
1/3x-4x+2+3=0
We multiply all the terms by the denominator
-4x*3x+2*3x+3*3x+1=0
Wy multiply elements
-12x^2+6x+9x+1=0
We add all the numbers together, and all the variables
-12x^2+15x+1=0
a = -12; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-12)·1
Δ = 273
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{273}}{2*-12}=\frac{-15-\sqrt{273}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{273}}{2*-12}=\frac{-15+\sqrt{273}}{-24} $
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