F(x)=-2x^2+3x+(3(8/4))

Solution for F(x)=-2x^2+3x+(3(8/4)) equation:

(F)=-2F^2+3F+(3(8/4))

We move all terms to the left:

(F)-(-2F^2+3F+(3(8/4)))=0

We add all the numbers together, and all the variables

-(-2F^2+3F+(32))+F=0

We add all the numbers together, and all the variables

-(-2F^2+3F+32)+F=0

We get rid of parentheses

2F^2-3F+F-32=0

We add all the numbers together, and all the variables

2F^2-2F-32=0

a = 2; b = -2; c = -32;
Δ = b2-4ac
Δ = -22-4·2·(-32)
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{65}}{2*2}=\frac{2-2\sqrt{65}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{65}}{2*2}=\frac{2+2\sqrt{65}}{4}
$