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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We get rid of parentheses

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

We calculate fractions


75w^2/60w^2+(-100w)/60w^2+(-24w)/60w^2=0

We multiply all the terms by the denominator


75w^2+(-100w)+(-24w)=0

We get rid of parentheses

75w^2-100w-24w=0

We add all the numbers together, and all the variables

75w^2-124w=0

a = 75; b = -124; c = 0;
Δ = b2-4ac
Δ = -1242-4·75·0
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-124}{2*75}=\frac{0}{150}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+124}{2*75}=\frac{248}{150}
=1+49/75
$