F(x)=x2-10x-24

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

(F)=F2-10F-24

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2+11F+24=0

a = -1; b = 11; c = +24;
Δ = b2-4ac
Δ = 112-4·(-1)·24
Δ = 217
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{-(11)-\sqrt{217}}{2*-1}=\frac{-11-\sqrt{217}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{217}}{2*-1}=\frac{-11+\sqrt{217}}{-2}
$