0=600-140x+6x^2

Solution for 0=600-140x+6x^2 equation:

0=600-140x+6x^2

We move all terms to the left:

0-(600-140x+6x^2)=0

We add all the numbers together, and all the variables

-(600-140x+6x^2)=0

We get rid of parentheses

-6x^2+140x-600=0

a = -6; b = 140; c = -600;
Δ = b2-4ac
Δ = 1402-4·(-6)·(-600)
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-20\sqrt{13}}{2*-6}=\frac{-140-20\sqrt{13}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+20\sqrt{13}}{2*-6}=\frac{-140+20\sqrt{13}}{-12}
$