F(x)=(x+8)(x-11)

Solution for F(x)=(x+8)(x-11) equation:

(F)=(F+8)(F-11)

We move all terms to the left:

(F)-((F+8)(F-11))=0

We multiply parentheses ..

-((+F^2-11F+8F-88))+F=0


We calculate terms in parentheses: -((+F^2-11F+8F-88)), so:

(+F^2-11F+8F-88)

We get rid of parentheses

F^2-11F+8F-88

We add all the numbers together, and all the variables

F^2-3F-88

Back to the equation:

-(F^2-3F-88)


We add all the numbers together, and all the variables

F-(F^2-3F-88)=0

We get rid of parentheses

-F^2+F+3F+88=0

We add all the numbers together, and all the variables

-1F^2+4F+88=0

a = -1; b = 4; c = +88;
Δ = b2-4ac
Δ = 42-4·(-1)·88
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{23}}{2*-1}=\frac{-4-4\sqrt{23}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{23}}{2*-1}=\frac{-4+4\sqrt{23}}{-2}
$