F(x)=9x^2-16x

Solution for F(x)=9x^2-16x equation:

(F)=9F^2-16F

We move all terms to the left:

(F)-(9F^2-16F)=0

We get rid of parentheses

-9F^2+F+16F=0

We add all the numbers together, and all the variables

-9F^2+17F=0

a = -9; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-9)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-9}=\frac{-34}{-18}
=1+8/9
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-9}=\frac{0}{-18}
=0
$