F(x)=(x+1)(x+11)

Solution for F(x)=(x+1)(x+11) equation:

(F)=(F+1)(F+11)

We move all terms to the left:

(F)-((F+1)(F+11))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((+F^2+11F+F+11)), so:

(+F^2+11F+F+11)

We get rid of parentheses

F^2+11F+F+11

We add all the numbers together, and all the variables

F^2+12F+11

Back to the equation:

-(F^2+12F+11)


We add all the numbers together, and all the variables

F-(F^2+12F+11)=0

We get rid of parentheses

-F^2+F-12F-11=0

We add all the numbers together, and all the variables

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

a = -1; b = -11; c = -11;
Δ = b2-4ac
Δ = -112-4·(-1)·(-11)
Δ = 77
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{77}}{2*-1}=\frac{11-\sqrt{77}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{77}}{2*-1}=\frac{11+\sqrt{77}}{-2}
$