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1/6x+2/3x=15
We move all terms to the left:
1/6x+2/3x-(15)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 3x!=0We calculate fractions
x!=0/3
x!=0
x∈R
3x/18x^2+12x/18x^2-15=0
We multiply all the terms by the denominator
3x+12x-15*18x^2=0
We add all the numbers together, and all the variables
15x-15*18x^2=0
Wy multiply elements
-270x^2+15x=0
a = -270; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-270)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-270}=\frac{-30}{-540} =1/18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-270}=\frac{0}{-540} =0 $
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