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3-7w-11=4/7w
We move all terms to the left:
3-7w-11-(4/7w)=0
Domain of the equation: 7w)!=0We add all the numbers together, and all the variables
w!=0/1
w!=0
w∈R
-7w-(+4/7w)+3-11=0
We add all the numbers together, and all the variables
-7w-(+4/7w)-8=0
We get rid of parentheses
-7w-4/7w-8=0
We multiply all the terms by the denominator
-7w*7w-8*7w-4=0
Wy multiply elements
-49w^2-56w-4=0
a = -49; b = -56; c = -4;
Δ = b2-4ac
Δ = -562-4·(-49)·(-4)
Δ = 2352
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-28\sqrt{3}}{2*-49}=\frac{56-28\sqrt{3}}{-98} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+28\sqrt{3}}{2*-49}=\frac{56+28\sqrt{3}}{-98} $
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