F(x)=X^2+12X+7

Solution for F(x)=X^2+12X+7 equation:

(F)=F^2+12F+7

We move all terms to the left:

(F)-(F^2+12F+7)=0

We get rid of parentheses

-F^2+F-12F-7=0

We add all the numbers together, and all the variables

-1F^2-11F-7=0

a = -1; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·(-1)·(-7)
Δ = 93
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{93}}{2*-1}=\frac{11-\sqrt{93}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{93}}{2*-1}=\frac{11+\sqrt{93}}{-2}
$