x(150-x)=2400

Solution for x(150-x)=2400 equation:

x(150-x)=2400

We move all terms to the left:

x(150-x)-(2400)=0

We add all the numbers together, and all the variables

x(-1x+150)-2400=0

We multiply parentheses

-1x^2+150x-2400=0

a = -1; b = 150; c = -2400;
Δ = b2-4ac
Δ = 1502-4·(-1)·(-2400)
Δ = 12900
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:

$\sqrt{\Delta}=\sqrt{12900}=\sqrt{100*129}=\sqrt{100}*\sqrt{129}=10\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-10\sqrt{129}}{2*-1}=\frac{-150-10\sqrt{129}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+10\sqrt{129}}{2*-1}=\frac{-150+10\sqrt{129}}{-2}
$