F(x)=4x^2+5x-1

Solution for F(x)=4x^2+5x-1 equation:

(F)=4F^2+5F-1

We move all terms to the left:

(F)-(4F^2+5F-1)=0

We get rid of parentheses

-4F^2+F-5F+1=0

We add all the numbers together, and all the variables

-4F^2-4F+1=0

a = -4; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-4)·1
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*-4}=\frac{4-4\sqrt{2}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*-4}=\frac{4+4\sqrt{2}}{-8}
$