F(x)=2x2+-6x+-9

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

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

We move all terms to the left:

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

We use the square of the difference formula

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2+7F+9=0

a = -2; b = 7; c = +9;
Δ = b2-4ac
Δ = 72-4·(-2)·9
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-2}=\frac{4}{-4}
=-1
$