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x(y+1)2=243y equation

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Numerical solution:

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The solution

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x*(y + 1)*2 = 243*y
2x(y+1)=243y2 x \left(y + 1\right) = 243 y
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Detail solution
Given the linear equation:
x*(y+1)*2 = 243*y

Expand brackets in the left part
xy*2+1*2 = 243*y

Divide both parts of the equation by 2 + 2*y
x = 243*y / (2 + 2*y)

We get the answer: x = 243*y/(2*(1 + y))
The solution of the parametric equation
Given the equation with a parameter:
2x(y+1)=243y2 x \left(y + 1\right) = 243 y
Коэффициент при x равен
2y+22 y + 2
then possible cases for y :
y<−1y < -1
y=−1y = -1
Consider all cases in more detail:
With
y<−1y < -1
the equation
486−2x=0486 - 2 x = 0
its solution
x=243x = 243
With
y=−1y = -1
the equation
243=0243 = 0
its solution
no solutions
The graph
Rapid solution [src] 
           /  y  \           /  y  \
     243*re|-----|   243*I*im|-----|
           \1 + y/           \1 + y/
x1 = ------------- + ---------------
           2                2
x1=243re⁡(yy+1)2+243iim⁡(yy+1)2x_{1} = \frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2} 
x1 = 243*re(y/(y + 1))/2 + 243*i*im(y/(y + 1))/2
Sum and product of roots [src] 
sum
      /  y  \           /  y  \
243*re|-----|   243*I*im|-----|
      \1 + y/           \1 + y/
------------- + ---------------
      2                2
243re⁡(yy+1)2+243iim⁡(yy+1)2\frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2} 
=
      /  y  \           /  y  \
243*re|-----|   243*I*im|-----|
      \1 + y/           \1 + y/
------------- + ---------------
      2                2
243re⁡(yy+1)2+243iim⁡(yy+1)2\frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2} 
product
      /  y  \           /  y  \
243*re|-----|   243*I*im|-----|
      \1 + y/           \1 + y/
------------- + ---------------
      2                2
243re⁡(yy+1)2+243iim⁡(yy+1)2\frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2} 
=
      /  y  \           /  y  \
243*re|-----|   243*I*im|-----|
      \1 + y/           \1 + y/
------------- + ---------------
      2                2
243re⁡(yy+1)2+243iim⁡(yy+1)2\frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2} 
243*re(y/(1 + y))/2 + 243*i*im(y/(1 + y))/2
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