n^2-200n+73=15000

Solution for n^2-200n+73=15000 equation:

n^2-200n+73=15000

We move all terms to the left:

n^2-200n+73-(15000)=0

We add all the numbers together, and all the variables

n^2-200n-14927=0

a = 1; b = -200; c = -14927;
Δ = b2-4ac
Δ = -2002-4·1·(-14927)
Δ = 99708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{99708}=\sqrt{4*24927}=\sqrt{4}*\sqrt{24927}=2\sqrt{24927}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-2\sqrt{24927}}{2*1}=\frac{200-2\sqrt{24927}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+2\sqrt{24927}}{2*1}=\frac{200+2\sqrt{24927}}{2}
$