F(x)=4x^2-17.2x-96

Solution for F(x)=4x^2-17.2x-96 equation:

(F)=4F^2-17.2F-96

We move all terms to the left:

(F)-(4F^2-17.2F-96)=0

We get rid of parentheses

-4F^2+F+17.2F+96=0

We add all the numbers together, and all the variables

-4F^2+18.2F+96=0

a = -4; b = 18.2; c = +96;
Δ = b2-4ac
Δ = 18.22-4·(-4)·96
Δ = 1867.24
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{-(18.2)-\sqrt{1867.24}}{2*-4}=\frac{-18.2-\sqrt{1867.24}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18.2)+\sqrt{1867.24}}{2*-4}=\frac{-18.2+\sqrt{1867.24}}{-8}
$