3=(a2-3a-9)

Solution for 3=(a2-3a-9) equation:

3=(a2-3a-9)

We move all terms to the left:

3-((a2-3a-9))=0

We add all the numbers together, and all the variables

-((+a^2-3a-9))+3=0


We calculate terms in parentheses: -((+a^2-3a-9)), so:

(+a^2-3a-9)

We get rid of parentheses

a^2-3a-9

Back to the equation:

-(a^2-3a-9)


We get rid of parentheses

-a^2+3a+9+3=0

We add all the numbers together, and all the variables

-1a^2+3a+12=0

a = -1; b = 3; c = +12;
Δ = b2-4ac
Δ = 32-4·(-1)·12
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{57}}{2*-1}=\frac{-3-\sqrt{57}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-1}=\frac{-3+\sqrt{57}}{-2}
$