F(x)=2x^2+12x+5

Solution for F(x)=2x^2+12x+5 equation:

(F)=2F^2+12F+5

We move all terms to the left:

(F)-(2F^2+12F+5)=0

We get rid of parentheses

-2F^2+F-12F-5=0

We add all the numbers together, and all the variables

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

a = -2; b = -11; c = -5;
Δ = b2-4ac
Δ = -112-4·(-2)·(-5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-9}{2*-2}=\frac{2}{-4}
=-1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*-2}=\frac{20}{-4}
=-5
$