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2/3x-12/3=-1/6x
We move all terms to the left:
2/3x-12/3-(-1/6x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(-1/6x)-4=0
We get rid of parentheses
2/3x+1/6x-4=0
We calculate fractions
12x/18x^2+3x/18x^2-4=0
We multiply all the terms by the denominator
12x+3x-4*18x^2=0
We add all the numbers together, and all the variables
15x-4*18x^2=0
Wy multiply elements
-72x^2+15x=0
a = -72; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-72)·0
Δ = 225
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-72}=\frac{-30}{-144} =5/24 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-72}=\frac{0}{-144} =0 $
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