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

Solution for F(2a)=2(2a^2)+3(2a)-6 equation:

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

We move all terms to the left:

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

We get rid of parentheses

-22F^2+2F-32F+6=0

We add all the numbers together, and all the variables

-22F^2-30F+6=0

a = -22; b = -30; c = +6;
Δ = b2-4ac
Δ = -302-4·(-22)·6
Δ = 1428
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:

$\sqrt{\Delta}=\sqrt{1428}=\sqrt{4*357}=\sqrt{4}*\sqrt{357}=2\sqrt{357}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{357}}{2*-22}=\frac{30-2\sqrt{357}}{-44}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{357}}{2*-22}=\frac{30+2\sqrt{357}}{-44}
$