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2/3y=15-y
We move all terms to the left:
2/3y-(15-y)=0
Domain of the equation: 3y!=0We add all the numbers together, and all the variables
y!=0/3
y!=0
y∈R
2/3y-(-1y+15)=0
We get rid of parentheses
2/3y+1y-15=0
We multiply all the terms by the denominator
1y*3y-15*3y+2=0
Wy multiply elements
3y^2-45y+2=0
a = 3; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·3·2
Δ = 2001
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2001}}{2*3}=\frac{45-\sqrt{2001}}{6} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2001}}{2*3}=\frac{45+\sqrt{2001}}{6} $
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