F(-2)=x^2+6(-2)-3

Solution for F(-2)=x^2+6(-2)-3 equation:

(-2)=F^2+6(-2)-3

We move all terms to the left:

(-2)-(F^2+6(-2)-3)=0

We add all the numbers together, and all the variables

-(F^2+6(-2)-3)-2=0


We calculate terms in parentheses: -(F^2+6(-2)-3), so:

F^2+6(-2)-3

determiningTheFunctionDomain
F^2-3+6(-2)

We add all the numbers together, and all the variables

F^2-15

Back to the equation:

-(F^2-15)


We get rid of parentheses

-F^2+15-2=0

We add all the numbers together, and all the variables

-1F^2+13=0

a = -1; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-1)·13
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{13}}{2*-1}=\frac{0-2\sqrt{13}}{-2}
=-\frac{2\sqrt{13}}{-2}
=-\frac{\sqrt{13}}{-1}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{13}}{2*-1}=\frac{0+2\sqrt{13}}{-2}
=\frac{2\sqrt{13}}{-2}
=\frac{\sqrt{13}}{-1}
$