X=200+12x+0.1x^2

Solution for X=200+12x+0.1x^2 equation:

X=200+12X+0.1X^2

We move all terms to the left:

X-(200+12X+0.1X^2)=0

We get rid of parentheses

-0.1X^2-12X+X-200=0

We add all the numbers together, and all the variables

-0.1X^2-11X-200=0

a = -0.1; b = -11; c = -200;
Δ = b2-4ac
Δ = -112-4·(-0.1)·(-200)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{41}}{2*-0.1}=\frac{11-\sqrt{41}}{-0.2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{41}}{2*-0.1}=\frac{11+\sqrt{41}}{-0.2}
$