F(x)=9x^2-54x-144

Solution for F(x)=9x^2-54x-144 equation:

(F)=9F^2-54F-144

We move all terms to the left:

(F)-(9F^2-54F-144)=0

We get rid of parentheses

-9F^2+F+54F+144=0

We add all the numbers together, and all the variables

-9F^2+55F+144=0

a = -9; b = 55; c = +144;
Δ = b2-4ac
Δ = 552-4·(-9)·144
Δ = 8209
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{-(55)-\sqrt{8209}}{2*-9}=\frac{-55-\sqrt{8209}}{-18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{8209}}{2*-9}=\frac{-55+\sqrt{8209}}{-18}
$