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4x-(y-1)^2=0 equation

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Numerical solution:

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The solution

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             2    
4*x - (y - 1)  = 0
4x−(y−1)2=04 x - \left(y - 1\right)^{2} = 0
Simplify
Detail solution
Given the linear equation:
4*x-(y-1)^2 = 0

Expand brackets in the left part
4*x-y+1^2 = 0

Looking for similar summands in the left part:
-(-1 + y)^2 + 4*x = 0

Move free summands (without x)
from left part to right part, we given:
4x−(y−1)2+1=14 x - \left(y - 1\right)^{2} + 1 = 1
Divide both parts of the equation by (1 - (-1 + y)^2 + 4*x)/x
x = 1 / ((1 - (-1 + y)^2 + 4*x)/x)

We get the answer: x = (-1 + y)^2/4
The graph
Rapid solution [src] 
         2                  2                       
       im (y)   (-1 + re(y))    I*(-1 + re(y))*im(y)
x1 = - ------ + ------------- + --------------------
         4            4                  2
x1=(re⁡(y)−1)24+i(re⁡(y)−1)im⁡(y)2−(im⁡(y))24x_{1} = \frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4} 
x1 = (re(y) - 1)^2/4 + i*(re(y) - 1)*im(y)/2 - im(y)^2/4
Sum and product of roots [src] 
sum
    2                  2                       
  im (y)   (-1 + re(y))    I*(-1 + re(y))*im(y)
- ------ + ------------- + --------------------
    4            4                  2
(re⁡(y)−1)24+i(re⁡(y)−1)im⁡(y)2−(im⁡(y))24\frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4} 
=
    2                  2                       
  im (y)   (-1 + re(y))    I*(-1 + re(y))*im(y)
- ------ + ------------- + --------------------
    4            4                  2
(re⁡(y)−1)24+i(re⁡(y)−1)im⁡(y)2−(im⁡(y))24\frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4} 
product
    2                  2                       
  im (y)   (-1 + re(y))    I*(-1 + re(y))*im(y)
- ------ + ------------- + --------------------
    4            4                  2
(re⁡(y)−1)24+i(re⁡(y)−1)im⁡(y)2−(im⁡(y))24\frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4} 
=
    2                  2                       
  im (y)   (-1 + re(y))    I*(-1 + re(y))*im(y)
- ------ + ------------- + --------------------
    4            4                  2
(re⁡(y)−1)24+i(re⁡(y)−1)im⁡(y)2−(im⁡(y))24\frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4} 
-im(y)^2/4 + (-1 + re(y))^2/4 + i*(-1 + re(y))*im(y)/2
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