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

Solution for F(0)=4x^2-5x equation:

(0)=4F^2-5F

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-4F^2+5F=0

a = -4; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-4)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-4}=\frac{0}{-8}
=0
$