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1/2y+8=1/5y+2
We move all terms to the left:
1/2y+8-(1/5y+2)=0
Domain of the equation: 2y!=0
y!=0/2
y!=0
y∈R
Domain of the equation: 5y+2)!=0We get rid of parentheses
y∈R
1/2y-1/5y-2+8=0
We calculate fractions
5y/10y^2+(-2y)/10y^2-2+8=0
We add all the numbers together, and all the variables
5y/10y^2+(-2y)/10y^2+6=0
We multiply all the terms by the denominator
5y+(-2y)+6*10y^2=0
Wy multiply elements
60y^2+5y+(-2y)=0
We get rid of parentheses
60y^2+5y-2y=0
We add all the numbers together, and all the variables
60y^2+3y=0
a = 60; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·60·0
Δ = 9
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{9}=3$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*60}=\frac{-6}{120} =-1/20 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*60}=\frac{0}{120} =0 $
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