150x-3x^2+600=0

Solution for 150x-3x^2+600=0 equation:

150x-3x^2+600=0

a = -3; b = 150; c = +600;
Δ = b2-4ac
Δ = 1502-4·(-3)·600
Δ = 29700
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:

$\sqrt{\Delta}=\sqrt{29700}=\sqrt{900*33}=\sqrt{900}*\sqrt{33}=30\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-30\sqrt{33}}{2*-3}=\frac{-150-30\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+30\sqrt{33}}{2*-3}=\frac{-150+30\sqrt{33}}{-6}
$