1/3a+1/4a=2/12

Solution for 1/3a+1/4a=2/12 equation:

1/3a+1/4a=2/12

We move all terms to the left:

1/3a+1/4a-(2/12)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

1/3a+1/4a-(+2/12)=0

We get rid of parentheses

1/3a+1/4a-2/12=0

We calculate fractions


(-96a^2)/144a^2+48a/144a^2+36a/144a^2=0

We multiply all the terms by the denominator


(-96a^2)+48a+36a=0

We add all the numbers together, and all the variables

(-96a^2)+84a=0

We get rid of parentheses

-96a^2+84a=0

a = -96; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-96)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-96}=\frac{-168}{-192}
=7/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-96}=\frac{0}{-192}
=0
$