F(x)=2x2+6x+3

Solution for F(x)=2x2+6x+3 equation:

(F)=2F^2+6F+3

We move all terms to the left:

(F)-(2F^2+6F+3)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·(-2)·(-3)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*-2}=\frac{4}{-4}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*-2}=\frac{6}{-4}
=-1+1/2
$