F(X)=x^2+11x-42

Solution for F(X)=x^2+11x-42 equation:

(F)=F^2+11F-42

We move all terms to the left:

(F)-(F^2+11F-42)=0

We get rid of parentheses

-F^2+F-11F+42=0

We add all the numbers together, and all the variables

-1F^2-10F+42=0

a = -1; b = -10; c = +42;
Δ = b2-4ac
Δ = -102-4·(-1)·42
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{67}}{2*-1}=\frac{10-2\sqrt{67}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{67}}{2*-1}=\frac{10+2\sqrt{67}}{-2}
$