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1-1+4/y=11/12y-1
We move all terms to the left:
1-1+4/y-(11/12y-1)=0
Domain of the equation: y!=0
y∈R
Domain of the equation: 12y-1)!=0We add all the numbers together, and all the variables
y∈R
4/y-(11/12y-1)=0
We get rid of parentheses
4/y-11/12y+1=0
We calculate fractions
48y/12y^2+(-11y)/12y^2+1=0
We multiply all the terms by the denominator
48y+(-11y)+1*12y^2=0
Wy multiply elements
12y^2+48y+(-11y)=0
We get rid of parentheses
12y^2+48y-11y=0
We add all the numbers together, and all the variables
12y^2+37y=0
a = 12; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·12·0
Δ = 1369
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{1369}=37$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*12}=\frac{-74}{24} =-3+1/12 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*12}=\frac{0}{24} =0 $
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