F(x)=x^2-12x-85

Solution for F(x)=x^2-12x-85 equation:

(F)=F^2-12F-85

We move all terms to the left:

(F)-(F^2-12F-85)=0

We get rid of parentheses

-F^2+F+12F+85=0

We add all the numbers together, and all the variables

-1F^2+13F+85=0

a = -1; b = 13; c = +85;
Δ = b2-4ac
Δ = 132-4·(-1)·85
Δ = 509
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{-(13)-\sqrt{509}}{2*-1}=\frac{-13-\sqrt{509}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{509}}{2*-1}=\frac{-13+\sqrt{509}}{-2}
$