F(x)=4x^2-9x

Solution for F(x)=4x^2-9x equation:

(F)=4F^2-9F

We move all terms to the left:

(F)-(4F^2-9F)=0

We get rid of parentheses

-4F^2+F+9F=0

We add all the numbers together, and all the variables

-4F^2+10F=0

a = -4; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-4)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-4}=\frac{-20}{-8}
=2+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-4}=\frac{0}{-8}
=0
$