x(60-3x)=150

Solution for x(60-3x)=150 equation:

x(60-3x)=150

We move all terms to the left:

x(60-3x)-(150)=0

We add all the numbers together, and all the variables

x(-3x+60)-150=0

We multiply parentheses

-3x^2+60x-150=0

a = -3; b = 60; c = -150;
Δ = b2-4ac
Δ = 602-4·(-3)·(-150)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-30\sqrt{2}}{2*-3}=\frac{-60-30\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+30\sqrt{2}}{2*-3}=\frac{-60+30\sqrt{2}}{-6}
$