1/3y+1/4y=5/12

Solution for 1/3y+1/4y=5/12 equation:

1/3y+1/4y=5/12

We move all terms to the left:

1/3y+1/4y-(5/12)=0


Domain of the equation: 3y!=0

y!=0/3

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

1/3y+1/4y-(+5/12)=0

We get rid of parentheses

1/3y+1/4y-5/12=0

We calculate fractions


(-240y^2)/144y^2+48y/144y^2+36y/144y^2=0

We multiply all the terms by the denominator


(-240y^2)+48y+36y=0

We add all the numbers together, and all the variables

(-240y^2)+84y=0

We get rid of parentheses

-240y^2+84y=0

a = -240; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-240)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-240}=\frac{-168}{-480}
=7/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-240}=\frac{0}{-480}
=0
$