F(x)=x^2-5x-3

Solution for F(x)=x^2-5x-3 equation:

(F)=F^2-5F-3

We move all terms to the left:

(F)-(F^2-5F-3)=0

We get rid of parentheses

-F^2+F+5F+3=0

We add all the numbers together, and all the variables

-1F^2+6F+3=0

a = -1; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-1)·3
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*-1}=\frac{-6-4\sqrt{3}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*-1}=\frac{-6+4\sqrt{3}}{-2}
$