F(x)=3x^2-16x+5

Solution for F(x)=3x^2-16x+5 equation:

(F)=3F^2-16F+5

We move all terms to the left:

(F)-(3F^2-16F+5)=0

We get rid of parentheses

-3F^2+F+16F-5=0

We add all the numbers together, and all the variables

-3F^2+17F-5=0

a = -3; b = 17; c = -5;
Δ = b2-4ac
Δ = 172-4·(-3)·(-5)
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{229}}{2*-3}=\frac{-17-\sqrt{229}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{229}}{2*-3}=\frac{-17+\sqrt{229}}{-6}
$