w-3/10=2w/6w+4

Solution for w-3/10=2w/6w+4 equation:

w-3/10=2w/6w+4

We move all terms to the left:

w-3/10-(2w/6w+4)=0


Domain of the equation: 6w+4)!=0

w∈R


We get rid of parentheses

w-2w/6w-4-3/10=0

We calculate fractions


w+(-20w)/60w+(-18w)/60w-4=0

We multiply all the terms by the denominator


w*60w+(-20w)+(-18w)-4*60w=0

Wy multiply elements

60w^2+(-20w)+(-18w)-240w=0

We get rid of parentheses

60w^2-20w-18w-240w=0

We add all the numbers together, and all the variables

60w^2-278w=0

a = 60; b = -278; c = 0;
Δ = b2-4ac
Δ = -2782-4·60·0
Δ = 77284
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{77284}=278$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-278)-278}{2*60}=\frac{0}{120}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-278)+278}{2*60}=\frac{556}{120}
=4+19/30
$