0=-12x^2+1440x-42000

Solution for 0=-12x^2+1440x-42000 equation:

0=-12x^2+1440x-42000

We move all terms to the left:

0-(-12x^2+1440x-42000)=0

We add all the numbers together, and all the variables

-(-12x^2+1440x-42000)=0

We get rid of parentheses

12x^2-1440x+42000=0

a = 12; b = -1440; c = +42000;
Δ = b2-4ac
Δ = -14402-4·12·42000
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1440)-240}{2*12}=\frac{1200}{24}
=50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1440)+240}{2*12}=\frac{1680}{24}
=70
$