3/2a+1/2a=4a+8

Solution for 3/2a+1/2a=4a+8 equation:

3/2a+1/2a=4a+8

We move all terms to the left:

3/2a+1/2a-(4a+8)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

3/2a+1/2a-4a-8=0

We multiply all the terms by the denominator


-4a*2a-8*2a+3+1=0

We add all the numbers together, and all the variables

-4a*2a-8*2a+4=0

Wy multiply elements

-8a^2-16a+4=0

a = -8; b = -16; c = +4;
Δ = b2-4ac
Δ = -162-4·(-8)·4
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{6}}{2*-8}=\frac{16-8\sqrt{6}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{6}}{2*-8}=\frac{16+8\sqrt{6}}{-16}
$