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30/y-18/2y=7
We move all terms to the left:
30/y-18/2y-(7)=0
Domain of the equation: y!=0
y∈R
Domain of the equation: 2y!=0We calculate fractions
y!=0/2
y!=0
y∈R
60y/2y^2+(-18y)/2y^2-7=0
We multiply all the terms by the denominator
60y+(-18y)-7*2y^2=0
Wy multiply elements
-14y^2+60y+(-18y)=0
We get rid of parentheses
-14y^2+60y-18y=0
We add all the numbers together, and all the variables
-14y^2+42y=0
a = -14; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-14)·0
Δ = 1764
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{1764}=42$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-14}=\frac{-84}{-28} =+3 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-14}=\frac{0}{-28} =0 $
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