F(-x)=x^2+9(-x)-4

Solution for F(-x)=x^2+9(-x)-4 equation:

(-F)=F^2+9(-F)-4

We move all terms to the left:

(-F)-(F^2+9(-F)-4)=0

We add all the numbers together, and all the variables

(-1F)-(F^2+9(-1F)-4)=0

We get rid of parentheses

-1F-(F^2+9(-1F)-4)=0


We calculate terms in parentheses: -(F^2+9(-1F)-4), so:

F^2+9(-1F)-4

We multiply parentheses

F^2-9F-4

Back to the equation:

-(F^2-9F-4)


We get rid of parentheses

-F^2-1F+9F+4=0

We add all the numbers together, and all the variables

-1F^2+8F+4=0

a = -1; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-1)·4
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{5}}{2*-1}=\frac{-8-4\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{5}}{2*-1}=\frac{-8+4\sqrt{5}}{-2}
$