F(x)=-4x^2+6x+2

Solution for F(x)=-4x^2+6x+2 equation:

(F)=-4F^2+6F+2

We move all terms to the left:

(F)-(-4F^2+6F+2)=0

We get rid of parentheses

4F^2-6F+F-2=0

We add all the numbers together, and all the variables

4F^2-5F-2=0

a = 4; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·4·(-2)
Δ = 57
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{-(-5)-\sqrt{57}}{2*4}=\frac{5-\sqrt{57}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*4}=\frac{5+\sqrt{57}}{8}
$