0=480x-13,500-x^2

Solution for 0=480x-13,500-x^2 equation:

0=480x-13.500-x^2

We move all terms to the left:

0-(480x-13.500-x^2)=0

We add all the numbers together, and all the variables

-(480x-13.500-x^2)=0

We get rid of parentheses

x^2-480x+13.500=0

We add all the numbers together, and all the variables

x^2-480x+13.5=0

a = 1; b = -480; c = +13.5;
Δ = b2-4ac
Δ = -4802-4·1·13.5
Δ = 230346
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{230346}=\sqrt{9*25594}=\sqrt{9}*\sqrt{25594}=3\sqrt{25594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-3\sqrt{25594}}{2*1}=\frac{480-3\sqrt{25594}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+3\sqrt{25594}}{2*1}=\frac{480+3\sqrt{25594}}{2}
$