1/6w+4+1/3w=10

Solution for 1/6w+4+1/3w=10 equation:

1/6w+4+1/3w=10

We move all terms to the left:

1/6w+4+1/3w-(10)=0


Domain of the equation: 6w!=0

w!=0/6

w!=0

w∈R



Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

1/6w+1/3w-6=0

We calculate fractions


3w/18w^2+6w/18w^2-6=0

We multiply all the terms by the denominator


3w+6w-6*18w^2=0

We add all the numbers together, and all the variables

9w-6*18w^2=0

Wy multiply elements

-108w^2+9w=0

a = -108; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-108)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-108}=\frac{-18}{-216}
=1/12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-108}=\frac{0}{-216}
=0
$