F(x)=-2x2+5x+9=3x2+6x-4

Solution for F(x)=-2x2+5x+9=3x2+6x-4 equation:

(F)=-2F^2+5F+9=3F^2+6F-4

We move all terms to the left:

(F)-(-2F^2+5F+9)=0

We get rid of parentheses

2F^2-5F+F-9=0

We add all the numbers together, and all the variables

2F^2-4F-9=0

a = 2; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·2·(-9)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{22}}{2*2}=\frac{4-2\sqrt{22}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{22}}{2*2}=\frac{4+2\sqrt{22}}{4}
$