f(-3)=X2+2X+3

Solution for f(-3)=X2+2X+3 equation:

f(-3)=f2+2f+3

We move all terms to the left:

f(-3)-(f2+2f+3)=0

We add all the numbers together, and all the variables

-(+f^2+2f+3)+f(-3)=0

We multiply parentheses

-(+f^2+2f+3)-3f=0

We get rid of parentheses

-f^2-2f-3f-3=0

We add all the numbers together, and all the variables

-1f^2-5f-3=0

a = -1; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·(-1)·(-3)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{13}}{2*-1}=\frac{5-\sqrt{13}}{-2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*-1}=\frac{5+\sqrt{13}}{-2}
$