F(x)=2(x+7)(x-3)

Solution for F(x)=2(x+7)(x-3) equation:

(F)=2(F+7)(F-3)

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We multiply parentheses

2F^2-6F+14F-42

We add all the numbers together, and all the variables

2F^2+8F-42

Back to the equation:

-(2F^2+8F-42)


We add all the numbers together, and all the variables

F-(2F^2+8F-42)=0

We get rid of parentheses

-2F^2+F-8F+42=0

We add all the numbers together, and all the variables

-2F^2-7F+42=0

a = -2; b = -7; c = +42;
Δ = b2-4ac
Δ = -72-4·(-2)·42
Δ = 385
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{385}}{2*-2}=\frac{7-\sqrt{385}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{385}}{2*-2}=\frac{7+\sqrt{385}}{-4}
$