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3.75y+18+54/3y=6.5+30
We move all terms to the left:
3.75y+18+54/3y-(6.5+30)=0
Domain of the equation: 3y!=0We add all the numbers together, and all the variables
y!=0/3
y!=0
y∈R
3.75y+54/3y+18-(36.5)=0
We add all the numbers together, and all the variables
3.75y+54/3y-18.5=0
We multiply all the terms by the denominator
(3.75y)*3y-(18.5)*3y+54=0
We add all the numbers together, and all the variables
(+3.75y)*3y-(18.5)*3y+54=0
We multiply parentheses
9y^2-55.5y+54=0
a = 9; b = -55.5; c = +54;
Δ = b2-4ac
Δ = -55.52-4·9·54
Δ = 1136.25
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{-(-55.5)-\sqrt{1136.25}}{2*9}=\frac{55.5-\sqrt{1136.25}}{18} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55.5)+\sqrt{1136.25}}{2*9}=\frac{55.5+\sqrt{1136.25}}{18} $
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