F(x)=-0.8x^2+2.4x+6

Solution for F(x)=-0.8x^2+2.4x+6 equation:

(F)=-0.8F^2+2.4F+6

We move all terms to the left:

(F)-(-0.8F^2+2.4F+6)=0

We get rid of parentheses

0.8F^2-2.4F+F-6=0

We add all the numbers together, and all the variables

0.8F^2-1.4F-6=0

a = 0.8; b = -1.4; c = -6;
Δ = b2-4ac
Δ = -1.42-4·0.8·(-6)
Δ = 21.16
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{-(-1.4)-\sqrt{21.16}}{2*0.8}=\frac{1.4-\sqrt{21.16}}{1.6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.4)+\sqrt{21.16}}{2*0.8}=\frac{1.4+\sqrt{21.16}}{1.6}
$