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2/w+2/3w=90
We move all terms to the left:
2/w+2/3w-(90)=0
Domain of the equation: w!=0
w∈R
Domain of the equation: 3w!=0We calculate fractions
w!=0/3
w!=0
w∈R
6w/3w^2+2w/3w^2-90=0
We multiply all the terms by the denominator
6w+2w-90*3w^2=0
We add all the numbers together, and all the variables
8w-90*3w^2=0
Wy multiply elements
-270w^2+8w=0
a = -270; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-270)·0
Δ = 64
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{64}=8$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-270}=\frac{-16}{-540} =4/135 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-270}=\frac{0}{-540} =0 $
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