400=1200x-2x^2

Solution for 400=1200x-2x^2 equation:

400=1200x-2x^2

We move all terms to the left:

400-(1200x-2x^2)=0

We get rid of parentheses

2x^2-1200x+400=0

a = 2; b = -1200; c = +400;
Δ = b2-4ac
Δ = -12002-4·2·400
Δ = 1436800
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:

$\sqrt{\Delta}=\sqrt{1436800}=\sqrt{1600*898}=\sqrt{1600}*\sqrt{898}=40\sqrt{898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-40\sqrt{898}}{2*2}=\frac{1200-40\sqrt{898}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+40\sqrt{898}}{2*2}=\frac{1200+40\sqrt{898}}{4}
$