F(x)=x2-5x-36

Solution for F(x)=x2-5x-36 equation:

(F)=F2-5F-36

We move all terms to the left:

(F)-(F2-5F-36)=0

We add all the numbers together, and all the variables

-(+F^2-5F-36)+F=0

We get rid of parentheses

-F^2+5F+F+36=0

We add all the numbers together, and all the variables

-1F^2+6F+36=0

a = -1; b = 6; c = +36;
Δ = b2-4ac
Δ = 62-4·(-1)·36
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*-1}=\frac{-6-6\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*-1}=\frac{-6+6\sqrt{5}}{-2}
$