F(x)=(x-7)(x+3)

Solution for F(x)=(x-7)(x+3) equation:

(F)=(F-7)(F+3)

We move all terms to the left:

(F)-((F-7)(F+3))=0

We multiply parentheses ..

-((+F^2+3F-7F-21))+F=0


We calculate terms in parentheses: -((+F^2+3F-7F-21)), so:

(+F^2+3F-7F-21)

We get rid of parentheses

F^2+3F-7F-21

We add all the numbers together, and all the variables

F^2-4F-21

Back to the equation:

-(F^2-4F-21)


We add all the numbers together, and all the variables

F-(F^2-4F-21)=0

We get rid of parentheses

-F^2+F+4F+21=0

We add all the numbers together, and all the variables

-1F^2+5F+21=0

a = -1; b = 5; c = +21;
Δ = b2-4ac
Δ = 52-4·(-1)·21
Δ = 109
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{-(5)-\sqrt{109}}{2*-1}=\frac{-5-\sqrt{109}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{109}}{2*-1}=\frac{-5+\sqrt{109}}{-2}
$