F(x)=(x+7)(x-13)

Solution for F(x)=(x+7)(x-13) equation:

(F)=(F+7)(F-13)

We move all terms to the left:

(F)-((F+7)(F-13))=0

We multiply parentheses ..

-((+F^2-13F+7F-91))+F=0


We calculate terms in parentheses: -((+F^2-13F+7F-91)), so:

(+F^2-13F+7F-91)

We get rid of parentheses

F^2-13F+7F-91

We add all the numbers together, and all the variables

F^2-6F-91

Back to the equation:

-(F^2-6F-91)


We add all the numbers together, and all the variables

F-(F^2-6F-91)=0

We get rid of parentheses

-F^2+F+6F+91=0

We add all the numbers together, and all the variables

-1F^2+7F+91=0

a = -1; b = 7; c = +91;
Δ = b2-4ac
Δ = 72-4·(-1)·91
Δ = 413
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{-(7)-\sqrt{413}}{2*-1}=\frac{-7-\sqrt{413}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{413}}{2*-1}=\frac{-7+\sqrt{413}}{-2}
$