1/3w+2/9w=10

Solution for 1/3w+2/9w=10 equation:

1/3w+2/9w=10

We move all terms to the left:

1/3w+2/9w-(10)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 9w!=0

w!=0/9

w!=0

w∈R


We calculate fractions


9w/27w^2+6w/27w^2-10=0

We multiply all the terms by the denominator


9w+6w-10*27w^2=0

We add all the numbers together, and all the variables

15w-10*27w^2=0

Wy multiply elements

-270w^2+15w=0

a = -270; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-270)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-270}=\frac{-30}{-540}
=1/18
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-270}=\frac{0}{-540}
=0
$