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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 17; c = -3;
Δ = b2-4ac
Δ = 172-4·(-2)·(-3)
Δ = 265
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{265}}{2*-2}=\frac{-17-\sqrt{265}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{265}}{2*-2}=\frac{-17+\sqrt{265}}{-4}
$