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2/5y-3/2y=-1/10
We move all terms to the left:
2/5y-3/2y-(-1/10)=0
Domain of the equation: 5y!=0
y!=0/5
y!=0
y∈R
Domain of the equation: 2y!=0We get rid of parentheses
y!=0/2
y!=0
y∈R
2/5y-3/2y+1/10=0
We calculate fractions
20y^2/100y^2+40y/100y^2+(-150y)/100y^2=0
We multiply all the terms by the denominator
20y^2+40y+(-150y)=0
We get rid of parentheses
20y^2+40y-150y=0
We add all the numbers together, and all the variables
20y^2-110y=0
a = 20; b = -110; c = 0;
Δ = b2-4ac
Δ = -1102-4·20·0
Δ = 12100
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{12100}=110$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-110}{2*20}=\frac{0}{40} =0 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+110}{2*20}=\frac{220}{40} =5+1/2 $
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