F(X)=-11x^2-5x+13

Solution for F(X)=-11x^2-5x+13 equation:

(F)=-11F^2-5F+13

We move all terms to the left:

(F)-(-11F^2-5F+13)=0

We get rid of parentheses

11F^2+5F+F-13=0

We add all the numbers together, and all the variables

11F^2+6F-13=0

a = 11; b = 6; c = -13;
Δ = b2-4ac
Δ = 62-4·11·(-13)
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{38}}{2*11}=\frac{-6-4\sqrt{38}}{22}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{38}}{2*11}=\frac{-6+4\sqrt{38}}{22}
$