3/2a-12=6+4a

Solution for 3/2a-12=6+4a equation:

3/2a-12=6+4a

We move all terms to the left:

3/2a-12-(6+4a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

3/2a-(4a+6)-12=0

We get rid of parentheses

3/2a-4a-6-12=0

We multiply all the terms by the denominator


-4a*2a-6*2a-12*2a+3=0

Wy multiply elements

-8a^2-12a-24a+3=0

We add all the numbers together, and all the variables

-8a^2-36a+3=0

a = -8; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·(-8)·3
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{87}}{2*-8}=\frac{36-4\sqrt{87}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{87}}{2*-8}=\frac{36+4\sqrt{87}}{-16}
$