610x-6000-x^2=0

Solution for 610x-6000-x^2=0 equation:

610x-6000-x^2=0

We add all the numbers together, and all the variables

-1x^2+610x-6000=0

a = -1; b = 610; c = -6000;
Δ = b2-4ac
Δ = 6102-4·(-1)·(-6000)
Δ = 348100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{348100}=590$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(610)-590}{2*-1}=\frac{-1200}{-2}
=+600
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(610)+590}{2*-1}=\frac{-20}{-2}
=+10
$