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3/yy-6=1/4y+10
We move all terms to the left:
3/yy-6-(1/4y+10)=0
Domain of the equation: yy!=0
y!=0/1
y!=0
y∈R
Domain of the equation: 4y+10)!=0We get rid of parentheses
y∈R
3/yy-1/4y-10-6=0
We calculate fractions
12y/4y^2+(-y)/4y^2-10-6=0
We add all the numbers together, and all the variables
12y/4y^2+(-1y)/4y^2-10-6=0
We add all the numbers together, and all the variables
12y/4y^2+(-1y)/4y^2-16=0
We multiply all the terms by the denominator
12y+(-1y)-16*4y^2=0
Wy multiply elements
-64y^2+12y+(-1y)=0
We get rid of parentheses
-64y^2+12y-1y=0
We add all the numbers together, and all the variables
-64y^2+11y=0
a = -64; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-64)·0
Δ = 121
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{121}=11$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-64}=\frac{-22}{-128} =11/64 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-64}=\frac{0}{-128} =0 $
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