X^2+40,000-580x=0

Solution for X^2+40,000-580x=0 equation:

X^2+40.000-580X=0

We add all the numbers together, and all the variables

X^2-580X+40=0

a = 1; b = -580; c = +40;
Δ = b2-4ac
Δ = -5802-4·1·40
Δ = 336240
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:

$\sqrt{\Delta}=\sqrt{336240}=\sqrt{144*2335}=\sqrt{144}*\sqrt{2335}=12\sqrt{2335}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-580)-12\sqrt{2335}}{2*1}=\frac{580-12\sqrt{2335}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-580)+12\sqrt{2335}}{2*1}=\frac{580+12\sqrt{2335}}{2}
$