n(n-3)=133

Solution for n(n-3)=133 equation:

n(n-3)=133

We move all terms to the left:

n(n-3)-(133)=0

We multiply parentheses

n^2-3n-133=0

a = 1; b = -3; c = -133;
Δ = b2-4ac
Δ = -32-4·1·(-133)
Δ = 541
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{541}}{2*1}=\frac{3-\sqrt{541}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{541}}{2*1}=\frac{3+\sqrt{541}}{2}
$