F(x)=9x^2-5x

Solution for F(x)=9x^2-5x equation:

(F)=9F^2-5F

We move all terms to the left:

(F)-(9F^2-5F)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-9F^2+6F=0

a = -9; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-9)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-9}=\frac{-12}{-18}
=2/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-9}=\frac{0}{-18}
=0
$