228/w=2w+6

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Solution for 228/w=2w+6 equation:



228/w=2w+6
We move all terms to the left:
228/w-(2w+6)=0
Domain of the equation: w!=0
w∈R
We get rid of parentheses
228/w-2w-6=0
We multiply all the terms by the denominator
-2w*w-6*w+228=0
We add all the numbers together, and all the variables
-6w-2w*w+228=0
Wy multiply elements
-2w^2-6w+228=0
a = -2; b = -6; c = +228;
Δ = b2-4ac
Δ = -62-4·(-2)·228
Δ = 1860
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:
$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{465}}{2*-2}=\frac{6-2\sqrt{465}}{-4} $
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{465}}{2*-2}=\frac{6+2\sqrt{465}}{-4} $

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