F(x)=(x+5)(X+11)

Solution for F(x)=(x+5)(X+11) equation:

(F)=(F+5)(F+11)

We move all terms to the left:

(F)-((F+5)(F+11))=0

We multiply parentheses ..

-((+F^2+11F+5F+55))+F=0


We calculate terms in parentheses: -((+F^2+11F+5F+55)), so:

(+F^2+11F+5F+55)

We get rid of parentheses

F^2+11F+5F+55

We add all the numbers together, and all the variables

F^2+16F+55

Back to the equation:

-(F^2+16F+55)


We add all the numbers together, and all the variables

F-(F^2+16F+55)=0

We get rid of parentheses

-F^2+F-16F-55=0

We add all the numbers together, and all the variables

-1F^2-15F-55=0

a = -1; b = -15; c = -55;
Δ = b2-4ac
Δ = -152-4·(-1)·(-55)
Δ = 5
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{-(-15)-\sqrt{5}}{2*-1}=\frac{15-\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{5}}{2*-1}=\frac{15+\sqrt{5}}{-2}
$