1/2y+1/4y=2+10

Solution for 1/2y+1/4y=2+10 equation:

1/2y+1/4y=2+10

We move all terms to the left:

1/2y+1/4y-(2+10)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y+1/4y-12=0

We calculate fractions


4y/8y^2+2y/8y^2-12=0

We multiply all the terms by the denominator


4y+2y-12*8y^2=0

We add all the numbers together, and all the variables

6y-12*8y^2=0

Wy multiply elements

-96y^2+6y=0

a = -96; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-96)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-96}=\frac{-12}{-192}
=1/16
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-96}=\frac{0}{-192}
=0
$