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7/4y-5/3=4/3y-7
We move all terms to the left:
7/4y-5/3-(4/3y-7)=0
Domain of the equation: 4y!=0
y!=0/4
y!=0
y∈R
Domain of the equation: 3y-7)!=0We get rid of parentheses
y∈R
7/4y-4/3y+7-5/3=0
We calculate fractions
189y/108y^2+(-16y)/108y^2+(-20y)/108y^2+7=0
We multiply all the terms by the denominator
189y+(-16y)+(-20y)+7*108y^2=0
Wy multiply elements
756y^2+189y+(-16y)+(-20y)=0
We get rid of parentheses
756y^2+189y-16y-20y=0
We add all the numbers together, and all the variables
756y^2+153y=0
a = 756; b = 153; c = 0;
Δ = b2-4ac
Δ = 1532-4·756·0
Δ = 23409
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{23409}=153$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(153)-153}{2*756}=\frac{-306}{1512} =-17/84 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(153)+153}{2*756}=\frac{0}{1512} =0 $
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