F(x)=5x^2-11x

Solution for F(x)=5x^2-11x equation:

(F)=5F^2-11F

We move all terms to the left:

(F)-(5F^2-11F)=0

We get rid of parentheses

-5F^2+F+11F=0

We add all the numbers together, and all the variables

-5F^2+12F=0

a = -5; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-5)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-5}=\frac{-24}{-10}
=2+2/5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-5}=\frac{0}{-10}
=0
$