F(x)=2x^2-11x+3

Solution for F(x)=2x^2-11x+3 equation:

(F)=2F^2-11F+3

We move all terms to the left:

(F)-(2F^2-11F+3)=0

We get rid of parentheses

-2F^2+F+11F-3=0

We add all the numbers together, and all the variables

-2F^2+12F-3=0

a = -2; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·(-2)·(-3)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{30}}{2*-2}=\frac{-12-2\sqrt{30}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{30}}{2*-2}=\frac{-12+2\sqrt{30}}{-4}
$