F(x)=x^2/240+15

Solution for F(x)=x^2/240+15 equation:

(F)=F^2/240+15

We move all terms to the left:

(F)-(F^2/240+15)=0

We get rid of parentheses

-F^2/240+F-15=0

We multiply all the terms by the denominator


-F^2+F*240-15*240=0

We add all the numbers together, and all the variables

-1F^2+F*240-3600=0

Wy multiply elements

-1F^2+240F-3600=0

a = -1; b = 240; c = -3600;
Δ = b2-4ac
Δ = 2402-4·(-1)·(-3600)
Δ = 43200
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:

$\sqrt{\Delta}=\sqrt{43200}=\sqrt{14400*3}=\sqrt{14400}*\sqrt{3}=120\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-120\sqrt{3}}{2*-1}=\frac{-240-120\sqrt{3}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+120\sqrt{3}}{2*-1}=\frac{-240+120\sqrt{3}}{-2}
$