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2/5y-4+7-1/10y=0
Domain of the equation: 5y!=0
y!=0/5
y!=0
y∈R
Domain of the equation: 10y!=0We add all the numbers together, and all the variables
y!=0/10
y!=0
y∈R
2/5y-1/10y+3=0
We calculate fractions
20y/50y^2+(-5y)/50y^2+3=0
We multiply all the terms by the denominator
20y+(-5y)+3*50y^2=0
Wy multiply elements
150y^2+20y+(-5y)=0
We get rid of parentheses
150y^2+20y-5y=0
We add all the numbers together, and all the variables
150y^2+15y=0
a = 150; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·150·0
Δ = 225
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{225}=15$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*150}=\frac{-30}{300} =-1/10 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*150}=\frac{0}{300} =0 $
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