F(5)=x2-10x+24

Solution for F(5)=x2-10x+24 equation:

(5)=F2-10F+24

We move all terms to the left:

(5)-(F2-10F+24)=0

We add all the numbers together, and all the variables

-(+F^2-10F+24)+5=0

We get rid of parentheses

-F^2+10F-24+5=0

We add all the numbers together, and all the variables

-1F^2+10F-19=0

a = -1; b = 10; c = -19;
Δ = b2-4ac
Δ = 102-4·(-1)·(-19)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{6}}{2*-1}=\frac{-10-2\sqrt{6}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{6}}{2*-1}=\frac{-10+2\sqrt{6}}{-2}
$