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1/2w+7=2w-w
We move all terms to the left:
1/2w+7-(2w-w)=0
Domain of the equation: 2w!=0We add all the numbers together, and all the variables
w!=0/2
w!=0
w∈R
1/2w-(+w)+7=0
We get rid of parentheses
1/2w-w+7=0
We multiply all the terms by the denominator
-w*2w+7*2w+1=0
Wy multiply elements
-2w^2+14w+1=0
a = -2; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-2)·1
Δ = 204
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{51}}{2*-2}=\frac{-14-2\sqrt{51}}{-4} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{51}}{2*-2}=\frac{-14+2\sqrt{51}}{-4} $
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