F(x)=4(x^2-64)

Solution for F(x)=4(x^2-64) equation:

(F)=4(F^2-64)

We move all terms to the left:

(F)-(4(F^2-64))=0


We calculate terms in parentheses: -(4(F^2-64)), so:

4(F^2-64)

We multiply parentheses

4F^2-256

Back to the equation:

-(4F^2-256)


We get rid of parentheses

-4F^2+F+256=0

a = -4; b = 1; c = +256;
Δ = b2-4ac
Δ = 12-4·(-4)·256
Δ = 4097
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{-(1)-\sqrt{4097}}{2*-4}=\frac{-1-\sqrt{4097}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{4097}}{2*-4}=\frac{-1+\sqrt{4097}}{-8}
$