1200=2184-188x+4x^2

Solution for 1200=2184-188x+4x^2 equation:

1200=2184-188x+4x^2

We move all terms to the left:

1200-(2184-188x+4x^2)=0

We get rid of parentheses

-4x^2+188x-2184+1200=0

We add all the numbers together, and all the variables

-4x^2+188x-984=0

a = -4; b = 188; c = -984;
Δ = b2-4ac
Δ = 1882-4·(-4)·(-984)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(188)-140}{2*-4}=\frac{-328}{-8}
=+41
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(188)+140}{2*-4}=\frac{-48}{-8}
=+6
$