F(x)=21x^2-x

Solution for F(x)=21x^2-x equation:

(F)=21F^2-F

We move all terms to the left:

(F)-(21F^2-F)=0

We get rid of parentheses

-21F^2+F+F=0

We add all the numbers together, and all the variables

-21F^2+2F=0

a = -21; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-21)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-21}=\frac{-4}{-42}
=2/21
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-21}=\frac{0}{-42}
=0
$