F(x)=9x^2-48x+64

Solution for F(x)=9x^2-48x+64 equation:

(F)=9F^2-48F+64

We move all terms to the left:

(F)-(9F^2-48F+64)=0

We get rid of parentheses

-9F^2+F+48F-64=0

We add all the numbers together, and all the variables

-9F^2+49F-64=0

a = -9; b = 49; c = -64;
Δ = b2-4ac
Δ = 492-4·(-9)·(-64)
Δ = 97
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{-(49)-\sqrt{97}}{2*-9}=\frac{-49-\sqrt{97}}{-18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{97}}{2*-9}=\frac{-49+\sqrt{97}}{-18}
$