F(x)=2x^2+9x-6

Solution for F(x)=2x^2+9x-6 equation:

(F)=2F^2+9F-6

We move all terms to the left:

(F)-(2F^2+9F-6)=0

We get rid of parentheses

-2F^2+F-9F+6=0

We add all the numbers together, and all the variables

-2F^2-8F+6=0

a = -2; b = -8; c = +6;
Δ = b2-4ac
Δ = -82-4·(-2)·6
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*-2}=\frac{8-4\sqrt{7}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*-2}=\frac{8+4\sqrt{7}}{-4}
$