F(x)=x2-5x-14

Solution for F(x)=x2-5x-14 equation:

(F)=F2-5F-14

We move all terms to the left:

(F)-(F2-5F-14)=0

We add all the numbers together, and all the variables

-(+F^2-5F-14)+F=0

We get rid of parentheses

-F^2+5F+F+14=0

We add all the numbers together, and all the variables

-1F^2+6F+14=0

a = -1; b = 6; c = +14;
Δ = b2-4ac
Δ = 62-4·(-1)·14
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{23}}{2*-1}=\frac{-6-2\sqrt{23}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{23}}{2*-1}=\frac{-6+2\sqrt{23}}{-2}
$