F(x)=x^2-14x+51

Solution for F(x)=x^2-14x+51 equation:

(F)=F^2-14F+51

We move all terms to the left:

(F)-(F^2-14F+51)=0

We get rid of parentheses

-F^2+F+14F-51=0

We add all the numbers together, and all the variables

-1F^2+15F-51=0

a = -1; b = 15; c = -51;
Δ = b2-4ac
Δ = 152-4·(-1)·(-51)
Δ = 21
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{-(15)-\sqrt{21}}{2*-1}=\frac{-15-\sqrt{21}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{21}}{2*-1}=\frac{-15+\sqrt{21}}{-2}
$