F(x)=4x2-8x-5

Solution for F(x)=4x2-8x-5 equation:

(F)=4F^2-8F-5

We move all terms to the left:

(F)-(4F^2-8F-5)=0

We get rid of parentheses

-4F^2+F+8F+5=0

We add all the numbers together, and all the variables

-4F^2+9F+5=0

a = -4; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·(-4)·5
Δ = 161
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{-(9)-\sqrt{161}}{2*-4}=\frac{-9-\sqrt{161}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{161}}{2*-4}=\frac{-9+\sqrt{161}}{-8}
$