-1/2a+1=-3-3a

Solution for -1/2a+1=-3-3a equation:

-1/2a+1=-3-3a

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6a^2+6a+2a-1=0

We add all the numbers together, and all the variables

6a^2+8a-1=0

a = 6; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·6·(-1)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*6}=\frac{-8-2\sqrt{22}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*6}=\frac{-8+2\sqrt{22}}{12}
$