F(x)=-9x2+7x+1

Solution for F(x)=-9x2+7x+1 equation:

(F)=-9F^2+7F+1

We move all terms to the left:

(F)-(-9F^2+7F+1)=0

We get rid of parentheses

9F^2-7F+F-1=0

We add all the numbers together, and all the variables

9F^2-6F-1=0

a = 9; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·9·(-1)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*9}=\frac{6-6\sqrt{2}}{18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*9}=\frac{6+6\sqrt{2}}{18}
$