4a=(-3)-a^2

Solution for 4a=(-3)-a^2 equation:

4a=(-3)-a^2

We move all terms to the left:

4a-((-3)-a^2)=0


We calculate terms in parentheses: -((-3)-a^2), so:

(-3)-a^2

determiningTheFunctionDomain
-a^2+(-3)

We add all the numbers together, and all the variables

-1a^2-3

Back to the equation:

-(-1a^2-3)


We get rid of parentheses

1a^2+4a+3=0

We add all the numbers together, and all the variables

a^2+4a+3=0

a = 1; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*1}=\frac{-6}{2}
=-3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*1}=\frac{-2}{2}
=-1
$