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1/6x-4=3+3/10x
We move all terms to the left:
1/6x-4-(3+3/10x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 10x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/6x-(3/10x+3)-4=0
We get rid of parentheses
1/6x-3/10x-3-4=0
We calculate fractions
10x/60x^2+(-18x)/60x^2-3-4=0
We add all the numbers together, and all the variables
10x/60x^2+(-18x)/60x^2-7=0
We multiply all the terms by the denominator
10x+(-18x)-7*60x^2=0
Wy multiply elements
-420x^2+10x+(-18x)=0
We get rid of parentheses
-420x^2+10x-18x=0
We add all the numbers together, and all the variables
-420x^2-8x=0
a = -420; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-420)·0
Δ = 64
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{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-420}=\frac{0}{-840} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-420}=\frac{16}{-840} =-2/105 $
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