F(x)=-16(x^2-3x-18)

Solution for F(x)=-16(x^2-3x-18) equation:

(F)=-16(F^2-3F-18)

We move all terms to the left:

(F)-(-16(F^2-3F-18))=0


We calculate terms in parentheses: -(-16(F^2-3F-18)), so:

-16(F^2-3F-18)

We multiply parentheses

-16F^2+48F+288

Back to the equation:

-(-16F^2+48F+288)


We get rid of parentheses

16F^2-48F+F-288=0

We add all the numbers together, and all the variables

16F^2-47F-288=0

a = 16; b = -47; c = -288;
Δ = b2-4ac
Δ = -472-4·16·(-288)
Δ = 20641
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{-(-47)-\sqrt{20641}}{2*16}=\frac{47-\sqrt{20641}}{32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{20641}}{2*16}=\frac{47+\sqrt{20641}}{32}
$