F(x)=-9x^2-4x+6

Solution for F(x)=-9x^2-4x+6 equation:

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

We move all terms to the left:

(F)-(-9F^2-4F+6)=0

We get rid of parentheses

9F^2+4F+F-6=0

We add all the numbers together, and all the variables

9F^2+5F-6=0

a = 9; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·9·(-6)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{241}}{2*9}=\frac{-5-\sqrt{241}}{18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{241}}{2*9}=\frac{-5+\sqrt{241}}{18}
$