200=x+3x+3x(x+3x)

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Solution for 200=x+3x+3x(x+3x) equation:



200=x+3x+3x(x+3x)
We move all terms to the left:
200-(x+3x+3x(x+3x))=0
We add all the numbers together, and all the variables
-(x+3x+3x(+4x))+200=0
We calculate terms in parentheses: -(x+3x+3x(+4x)), so:
x+3x+3x(+4x)
We add all the numbers together, and all the variables
4x+3x(+4x)
We multiply parentheses
12x^2+4x
Back to the equation:
-(12x^2+4x)
We get rid of parentheses
-12x^2-4x+200=0
a = -12; b = -4; c = +200;
Δ = b2-4ac
Δ = -42-4·(-12)·200
Δ = 9616
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:
$\sqrt{\Delta}=\sqrt{9616}=\sqrt{16*601}=\sqrt{16}*\sqrt{601}=4\sqrt{601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{601}}{2*-12}=\frac{4-4\sqrt{601}}{-24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{601}}{2*-12}=\frac{4+4\sqrt{601}}{-24} $

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