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2/3y+3/8y=5
We move all terms to the left:
2/3y+3/8y-(5)=0
Domain of the equation: 3y!=0
y!=0/3
y!=0
y∈R
Domain of the equation: 8y!=0We calculate fractions
y!=0/8
y!=0
y∈R
16y/24y^2+9y/24y^2-5=0
We multiply all the terms by the denominator
16y+9y-5*24y^2=0
We add all the numbers together, and all the variables
25y-5*24y^2=0
Wy multiply elements
-120y^2+25y=0
a = -120; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-120)·0
Δ = 625
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{625}=25$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-120}=\frac{-50}{-240} =5/24 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-120}=\frac{0}{-240} =0 $
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