1200=x*(150-x)

Solution for 1200=x*(150-x) equation:

1200=x(150-x)

We move all terms to the left:

1200-(x(150-x))=0

We add all the numbers together, and all the variables

-(x(-1x+150))+1200=0


We calculate terms in parentheses: -(x(-1x+150)), so:

x(-1x+150)

We multiply parentheses

-1x^2+150x

Back to the equation:

-(-1x^2+150x)


We get rid of parentheses

1x^2-150x+1200=0

We add all the numbers together, and all the variables

x^2-150x+1200=0

a = 1; b = -150; c = +1200;
Δ = b2-4ac
Δ = -1502-4·1·1200
Δ = 17700
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:

$\sqrt{\Delta}=\sqrt{17700}=\sqrt{100*177}=\sqrt{100}*\sqrt{177}=10\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-10\sqrt{177}}{2*1}=\frac{150-10\sqrt{177}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+10\sqrt{177}}{2*1}=\frac{150+10\sqrt{177}}{2}
$