n^2-n=200

Solution for n^2-n=200 equation:

n^2-n=200

We move all terms to the left:

n^2-n-(200)=0

We add all the numbers together, and all the variables

n^2-1n-200=0

a = 1; b = -1; c = -200;
Δ = b2-4ac
Δ = -12-4·1·(-200)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{89}}{2*1}=\frac{1-3\sqrt{89}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{89}}{2*1}=\frac{1+3\sqrt{89}}{2}
$