150n(n-3)=900

Solution for 150n(n-3)=900 equation:

150n(n-3)=900

We move all terms to the left:

150n(n-3)-(900)=0

We multiply parentheses

150n^2-450n-900=0

a = 150; b = -450; c = -900;
Δ = b2-4ac
Δ = -4502-4·150·(-900)
Δ = 742500
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:

$\sqrt{\Delta}=\sqrt{742500}=\sqrt{22500*33}=\sqrt{22500}*\sqrt{33}=150\sqrt{33}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-150\sqrt{33}}{2*150}=\frac{450-150\sqrt{33}}{300}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+150\sqrt{33}}{2*150}=\frac{450+150\sqrt{33}}{300}
$