-1/2a-5=a+4

Solution for -1/2a-5=a+4 equation:

-1/2a-5=a+4

We move all terms to the left:

-1/2a-5-(a+4)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

-1/2a-a-4-5=0

We multiply all the terms by the denominator


-a*2a-4*2a-5*2a-1=0

Wy multiply elements

-2a^2-8a-10a-1=0

We add all the numbers together, and all the variables

-2a^2-18a-1=0

a = -2; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·(-2)·(-1)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{79}}{2*-2}=\frac{18-2\sqrt{79}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{79}}{2*-2}=\frac{18+2\sqrt{79}}{-4}
$