F(x)=x^2+12x-5

Solution for F(x)=x^2+12x-5 equation:

(F)=F^2+12F-5

We move all terms to the left:

(F)-(F^2+12F-5)=0

We get rid of parentheses

-F^2+F-12F+5=0

We add all the numbers together, and all the variables

-1F^2-11F+5=0

a = -1; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·(-1)·5
Δ = 141
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{141}}{2*-1}=\frac{11-\sqrt{141}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{141}}{2*-1}=\frac{11+\sqrt{141}}{-2}
$