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3/4y+8=-1/3y+6
We move all terms to the left:
3/4y+8-(-1/3y+6)=0
Domain of the equation: 4y!=0
y!=0/4
y!=0
y∈R
Domain of the equation: 3y+6)!=0We get rid of parentheses
y∈R
3/4y+1/3y-6+8=0
We calculate fractions
9y/12y^2+4y/12y^2-6+8=0
We add all the numbers together, and all the variables
9y/12y^2+4y/12y^2+2=0
We multiply all the terms by the denominator
9y+4y+2*12y^2=0
We add all the numbers together, and all the variables
13y+2*12y^2=0
Wy multiply elements
24y^2+13y=0
a = 24; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·24·0
Δ = 169
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{169}=13$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*24}=\frac{-26}{48} =-13/24 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*24}=\frac{0}{48} =0 $
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