6-1/3w+7/5w=4

Solution for 6-1/3w+7/5w=4 equation:

6-1/3w+7/5w=4

We move all terms to the left:

6-1/3w+7/5w-(4)=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 add all the numbers together, and all the variables

-1/3w+7/5w+2=0

We calculate fractions


(-5w)/15w^2+21w/15w^2+2=0

We multiply all the terms by the denominator


(-5w)+21w+2*15w^2=0

We add all the numbers together, and all the variables

21w+(-5w)+2*15w^2=0

Wy multiply elements

30w^2+21w+(-5w)=0

We get rid of parentheses

30w^2+21w-5w=0

We add all the numbers together, and all the variables

30w^2+16w=0

a = 30; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·30·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*30}=\frac{-32}{60}
=-8/15
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*30}=\frac{0}{60}
=0
$