150x-x^2=1200

Solution for 150x-x^2=1200 equation:

150x-x^2=1200

We move all terms to the left:

150x-x^2-(1200)=0

We add all the numbers together, and all the variables

-1x^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}
$