F(x)=x^2-18x+77

Solution for F(x)=x^2-18x+77 equation:

(F)=F^2-18F+77

We move all terms to the left:

(F)-(F^2-18F+77)=0

We get rid of parentheses

-F^2+F+18F-77=0

We add all the numbers together, and all the variables

-1F^2+19F-77=0

a = -1; b = 19; c = -77;
Δ = b2-4ac
Δ = 192-4·(-1)·(-77)
Δ = 53
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{-(19)-\sqrt{53}}{2*-1}=\frac{-19-\sqrt{53}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{53}}{2*-1}=\frac{-19+\sqrt{53}}{-2}
$