F(x)=x^2+9x-19

Solution for F(x)=x^2+9x-19 equation:

(F)=F^2+9F-19

We move all terms to the left:

(F)-(F^2+9F-19)=0

We get rid of parentheses

-F^2+F-9F+19=0

We add all the numbers together, and all the variables

-1F^2-8F+19=0

a = -1; b = -8; c = +19;
Δ = b2-4ac
Δ = -82-4·(-1)·19
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{35}}{2*-1}=\frac{8-2\sqrt{35}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{35}}{2*-1}=\frac{8+2\sqrt{35}}{-2}
$