F(x)=x2+17x-60

Solution for F(x)=x2+17x-60 equation:

(F)=F2+17F-60

We move all terms to the left:

(F)-(F2+17F-60)=0

We add all the numbers together, and all the variables

-(+F^2+17F-60)+F=0

We get rid of parentheses

-F^2-17F+F+60=0

We add all the numbers together, and all the variables

-1F^2-16F+60=0

a = -1; b = -16; c = +60;
Δ = b2-4ac
Δ = -162-4·(-1)·60
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{31}}{2*-1}=\frac{16-4\sqrt{31}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{31}}{2*-1}=\frac{16+4\sqrt{31}}{-2}
$