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2/7y-5/3y=-5/2
We move all terms to the left:
2/7y-5/3y-(-5/2)=0
Domain of the equation: 7y!=0
y!=0/7
y!=0
y∈R
Domain of the equation: 3y!=0We get rid of parentheses
y!=0/3
y!=0
y∈R
2/7y-5/3y+5/2=0
We calculate fractions
315y^2/84y^2+24y/84y^2+(-140y)/84y^2=0
We multiply all the terms by the denominator
315y^2+24y+(-140y)=0
We get rid of parentheses
315y^2+24y-140y=0
We add all the numbers together, and all the variables
315y^2-116y=0
a = 315; b = -116; c = 0;
Δ = b2-4ac
Δ = -1162-4·315·0
Δ = 13456
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{13456}=116$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-116}{2*315}=\frac{0}{630} =0 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+116}{2*315}=\frac{232}{630} =116/315 $
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