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7/10w-18=51/8w
We move all terms to the left:
7/10w-18-(51/8w)=0
Domain of the equation: 10w!=0
w!=0/10
w!=0
w∈R
Domain of the equation: 8w)!=0We add all the numbers together, and all the variables
w!=0/1
w!=0
w∈R
7/10w-(+51/8w)-18=0
We get rid of parentheses
7/10w-51/8w-18=0
We calculate fractions
56w/80w^2+(-510w)/80w^2-18=0
We multiply all the terms by the denominator
56w+(-510w)-18*80w^2=0
Wy multiply elements
-1440w^2+56w+(-510w)=0
We get rid of parentheses
-1440w^2+56w-510w=0
We add all the numbers together, and all the variables
-1440w^2-454w=0
a = -1440; b = -454; c = 0;
Δ = b2-4ac
Δ = -4542-4·(-1440)·0
Δ = 206116
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{206116}=454$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-454)-454}{2*-1440}=\frac{0}{-2880} =0 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-454)+454}{2*-1440}=\frac{908}{-2880} =-227/720 $
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