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1/4w+8=1/2w-6
We move all terms to the left:
1/4w+8-(1/2w-6)=0
Domain of the equation: 4w!=0
w!=0/4
w!=0
w∈R
Domain of the equation: 2w-6)!=0We get rid of parentheses
w∈R
1/4w-1/2w+6+8=0
We calculate fractions
2w/8w^2+(-4w)/8w^2+6+8=0
We add all the numbers together, and all the variables
2w/8w^2+(-4w)/8w^2+14=0
We multiply all the terms by the denominator
2w+(-4w)+14*8w^2=0
Wy multiply elements
112w^2+2w+(-4w)=0
We get rid of parentheses
112w^2+2w-4w=0
We add all the numbers together, and all the variables
112w^2-2w=0
a = 112; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·112·0
Δ = 4
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{4}=2$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*112}=\frac{0}{224} =0 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*112}=\frac{4}{224} =1/56 $
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