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7/4w-7/3=-5/3w-1
We move all terms to the left:
7/4w-7/3-(-5/3w-1)=0
Domain of the equation: 4w!=0
w!=0/4
w!=0
w∈R
Domain of the equation: 3w-1)!=0We get rid of parentheses
w∈R
7/4w+5/3w+1-7/3=0
We calculate fractions
189w/108w^2+20w/108w^2+(-28w)/108w^2+1=0
We multiply all the terms by the denominator
189w+20w+(-28w)+1*108w^2=0
We add all the numbers together, and all the variables
209w+(-28w)+1*108w^2=0
Wy multiply elements
108w^2+209w+(-28w)=0
We get rid of parentheses
108w^2+209w-28w=0
We add all the numbers together, and all the variables
108w^2+181w=0
a = 108; b = 181; c = 0;
Δ = b2-4ac
Δ = 1812-4·108·0
Δ = 32761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{32761}=181$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(181)-181}{2*108}=\frac{-362}{216} =-1+73/108 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(181)+181}{2*108}=\frac{0}{216} =0 $
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