3+1/4a=12+a

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

3+1/4a=12+a

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-a*4a-12*4a+3*4a+1=0

Wy multiply elements

-4a^2-48a+12a+1=0

We add all the numbers together, and all the variables

-4a^2-36a+1=0

a = -4; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·(-4)·1
Δ = 1312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{82}}{2*-4}=\frac{36-4\sqrt{82}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{82}}{2*-4}=\frac{36+4\sqrt{82}}{-8}
$