F(x)=x2-6x-60

Solution for F(x)=x2-6x-60 equation:

(F)=F2-6F-60

We move all terms to the left:

(F)-(F2-6F-60)=0

We add all the numbers together, and all the variables

-(+F^2-6F-60)+F=0

We get rid of parentheses

-F^2+6F+F+60=0

We add all the numbers together, and all the variables

-1F^2+7F+60=0

a = -1; b = 7; c = +60;
Δ = b2-4ac
Δ = 72-4·(-1)·60
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*-1}=\frac{-24}{-2}
=+12
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*-1}=\frac{10}{-2}
=-5
$