F(2)=2x^2+6x+5

Solution for F(2)=2x^2+6x+5 equation:

(2)=2F^2+6F+5

We move all terms to the left:

(2)-(2F^2+6F+5)=0

We get rid of parentheses

-2F^2-6F-5+2=0

We add all the numbers together, and all the variables

-2F^2-6F-3=0

a = -2; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·(-2)·(-3)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*-2}=\frac{6-2\sqrt{3}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*-2}=\frac{6+2\sqrt{3}}{-4}
$