-5/w-3/5w=-4/3

Solution for -5/w-3/5w=-4/3 equation:

-5/w-3/5w=-4/3

We move all terms to the left:

-5/w-3/5w-(-4/3)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We get rid of parentheses

-5/w-3/5w+4/3=0

We calculate fractions


100w^2/45w^2+(-225w)/45w^2+(-27w)/45w^2=0

We multiply all the terms by the denominator


100w^2+(-225w)+(-27w)=0

We get rid of parentheses

100w^2-225w-27w=0

We add all the numbers together, and all the variables

100w^2-252w=0

a = 100; b = -252; c = 0;
Δ = b2-4ac
Δ = -2522-4·100·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-252}{2*100}=\frac{0}{200}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+252}{2*100}=\frac{504}{200}
=2+13/25
$