F(x)=(x-4)(2x+1)

Solution for F(x)=(x-4)(2x+1) equation:

(F)=(F-4)(2F+1)

We move all terms to the left:

(F)-((F-4)(2F+1))=0

We multiply parentheses ..

-((+2F^2+F-8F-4))+F=0


We calculate terms in parentheses: -((+2F^2+F-8F-4)), so:

(+2F^2+F-8F-4)

We get rid of parentheses

2F^2+F-8F-4

We add all the numbers together, and all the variables

2F^2-7F-4

Back to the equation:

-(2F^2-7F-4)


We add all the numbers together, and all the variables

F-(2F^2-7F-4)=0

We get rid of parentheses

-2F^2+F+7F+4=0

We add all the numbers together, and all the variables

-2F^2+8F+4=0

a = -2; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-2)·4
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*-2}=\frac{-8-4\sqrt{6}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*-2}=\frac{-8+4\sqrt{6}}{-4}
$