-1/2a-2=a+1

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

-1/2a-2=a+1

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

-1/2a-a-1-2=0

We multiply all the terms by the denominator


-a*2a-1*2a-2*2a-1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·(-2)·(-1)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{7}}{2*-2}=\frac{6-2\sqrt{7}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{7}}{2*-2}=\frac{6+2\sqrt{7}}{-4}
$