-2/3w-1/5=2/5w-6

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Solution for -2/3w-1/5=2/5w-6 equation:



-2/3w-1/5=2/5w-6
We move all terms to the left:
-2/3w-1/5-(2/5w-6)=0
Domain of the equation: 3w!=0
w!=0/3
w!=0
w∈R
Domain of the equation: 5w-6)!=0
w∈R
We get rid of parentheses
-2/3w-2/5w+6-1/5=0
We calculate fractions
(-250w)/375w^2+(-6w)/375w^2+(-3w)/375w^2+6=0
We multiply all the terms by the denominator
(-250w)+(-6w)+(-3w)+6*375w^2=0
Wy multiply elements
2250w^2+(-250w)+(-6w)+(-3w)=0
We get rid of parentheses
2250w^2-250w-6w-3w=0
We add all the numbers together, and all the variables
2250w^2-259w=0
a = 2250; b = -259; c = 0;
Δ = b2-4ac
Δ = -2592-4·2250·0
Δ = 67081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67081}=259$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-259)-259}{2*2250}=\frac{0}{4500} =0 $
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-259)+259}{2*2250}=\frac{518}{4500} =259/2250 $

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