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2/37y+y=31
We move all terms to the left:
2/37y+y-(31)=0
Domain of the equation: 37y!=0We add all the numbers together, and all the variables
y!=0/37
y!=0
y∈R
y+2/37y-31=0
We multiply all the terms by the denominator
y*37y-31*37y+2=0
Wy multiply elements
37y^2-1147y+2=0
a = 37; b = -1147; c = +2;
Δ = b2-4ac
Δ = -11472-4·37·2
Δ = 1315313
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1147)-\sqrt{1315313}}{2*37}=\frac{1147-\sqrt{1315313}}{74} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1147)+\sqrt{1315313}}{2*37}=\frac{1147+\sqrt{1315313}}{74} $
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