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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2-6F+12=0

a = -1; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-1)·12
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-1}=\frac{6-2\sqrt{21}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-1}=\frac{6+2\sqrt{21}}{-2}
$