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

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

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

We move all terms to the left:

1/3w+3-(2/5w-5)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 5w-5)!=0

w∈R


We get rid of parentheses

1/3w-2/5w+5+3=0

We calculate fractions


5w/15w^2+(-6w)/15w^2+5+3=0

We add all the numbers together, and all the variables

5w/15w^2+(-6w)/15w^2+8=0

We multiply all the terms by the denominator


5w+(-6w)+8*15w^2=0

Wy multiply elements

120w^2+5w+(-6w)=0

We get rid of parentheses

120w^2+5w-6w=0

We add all the numbers together, and all the variables

120w^2-1w=0

a = 120; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·120·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*120}=\frac{0}{240}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*120}=\frac{2}{240}
=1/120
$