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1/6y-1/2=3-1/2y
We move all terms to the left:
1/6y-1/2-(3-1/2y)=0
Domain of the equation: 6y!=0
y!=0/6
y!=0
y∈R
Domain of the equation: 2y)!=0We add all the numbers together, and all the variables
y!=0/1
y!=0
y∈R
1/6y-(-1/2y+3)-1/2=0
We get rid of parentheses
1/6y+1/2y-3-1/2=0
We calculate fractions
8y/48y^2+6y/48y^2+(-6y)/48y^2-3=0
We multiply all the terms by the denominator
8y+6y+(-6y)-3*48y^2=0
We add all the numbers together, and all the variables
14y+(-6y)-3*48y^2=0
Wy multiply elements
-144y^2+14y+(-6y)=0
We get rid of parentheses
-144y^2+14y-6y=0
We add all the numbers together, and all the variables
-144y^2+8y=0
a = -144; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-144)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{64}=8$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-144}=\frac{-16}{-288} =1/18 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-144}=\frac{0}{-288} =0 $
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