1/6y+1/2y=10

Solution for 1/6y+1/2y=10 equation:

1/6y+1/2y=10

We move all terms to the left:

1/6y+1/2y-(10)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We calculate fractions


2y/12y^2+6y/12y^2-10=0

We multiply all the terms by the denominator


2y+6y-10*12y^2=0

We add all the numbers together, and all the variables

8y-10*12y^2=0

Wy multiply elements

-120y^2+8y=0

a = -120; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-120)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-120}=\frac{-16}{-240}
=1/15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-120}=\frac{0}{-240}
=0
$