F=16z2-64-(-4z-8)(7z+9)

Solution for F=16z2-64-(-4z-8)(7z+9) equation:

=16F^2-64-(-4F-8)(7F+9)

We move all terms to the left:

-(16F^2-64-(-4F-8)(7F+9))=0

We multiply parentheses ..

-(16F^2-64-(-28F^2-36F-56F-72))=0


We calculate terms in parentheses: -(16F^2-64-(-28F^2-36F-56F-72)), so:

16F^2-64-(-28F^2-36F-56F-72)

determiningTheFunctionDomain
16F^2-(-28F^2-36F-56F-72)-64

We get rid of parentheses

16F^2+28F^2+36F+56F+72-64

We add all the numbers together, and all the variables

44F^2+92F+8

Back to the equation:

-(44F^2+92F+8)


We get rid of parentheses

-44F^2-92F-8=0

a = -44; b = -92; c = -8;
Δ = b2-4ac
Δ = -922-4·(-44)·(-8)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-84}{2*-44}=\frac{8}{-88}
=-1/11
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+84}{2*-44}=\frac{176}{-88}
=-2
$