1/3y+2/9y=10

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

1/3y+2/9y=10

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

15y-10*27y^2=0

Wy multiply elements

-270y^2+15y=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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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