F(x)=-4x2-6x+8

Solution for F(x)=-4x2-6x+8 equation:

(F)=-4F^2-6F+8

We move all terms to the left:

(F)-(-4F^2-6F+8)=0

We get rid of parentheses

4F^2+6F+F-8=0

We add all the numbers together, and all the variables

4F^2+7F-8=0

a = 4; b = 7; c = -8;
Δ = b2-4ac
Δ = 72-4·4·(-8)
Δ = 177
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{-(7)-\sqrt{177}}{2*4}=\frac{-7-\sqrt{177}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{177}}{2*4}=\frac{-7+\sqrt{177}}{8}
$