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1/3y+1/6y=9/5
We move all terms to the left:
1/3y+1/6y-(9/5)=0
Domain of the equation: 3y!=0
y!=0/3
y!=0
y∈R
Domain of the equation: 6y!=0We add all the numbers together, and all the variables
y!=0/6
y!=0
y∈R
1/3y+1/6y-(+9/5)=0
We get rid of parentheses
1/3y+1/6y-9/5=0
We calculate fractions
(-972y^2)/450y^2+150y/450y^2+75y/450y^2=0
We multiply all the terms by the denominator
(-972y^2)+150y+75y=0
We add all the numbers together, and all the variables
(-972y^2)+225y=0
We get rid of parentheses
-972y^2+225y=0
a = -972; b = 225; c = 0;
Δ = b2-4ac
Δ = 2252-4·(-972)·0
Δ = 50625
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{50625}=225$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-225}{2*-972}=\frac{-450}{-1944} =25/108 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+225}{2*-972}=\frac{0}{-1944} =0 $
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