This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
https://en.wikipedia.org/wiki/Quadratic_formula#Derivations_of_the_formula
Clicking on the step index will take you to the page where you can edit that step.
Index  Inference Rule  Input latex  Feeds latex  Output latex  step validity  dimension check  unit check  notes 

10  subtract X from both sides 



LHS diff is 0 RHS diff is sqrt((pdg1939**2  4*pdg4231*pdg9139)/pdg9139**2) 
5982958249:
9582958293: 
5982958249:
9582958293: 

10.5  subtract X from both sides 



LHS diff is 0 RHS diff is sqrt((pdg1939**2  4*pdg4231*pdg9139)/pdg9139**2) 
9582958294:
5982958248: 
9582958294:
5982958248: 

11  simplify 



LHS diff is 0 RHS diff is (pdg9139*sqrt((pdg1939**2  4*pdg4231*pdg9139)/pdg9139**2) + sqrt(pdg1939**2  4*pdg4231*pdg9139))/(2*pdg9139) 
5982958248:
9999999968: 
5982958248:
9999999968: 

11.5  simplify 



LHS diff is 0 RHS diff is (pdg9139*sqrt((pdg1939**2  4*pdg4231*pdg9139)/pdg9139**2)  sqrt(pdg1939**2  4*pdg4231*pdg9139))/(2*pdg9139) 
9582958293:
9999999969: 
9582958293:
9999999969: 

5  add X to both sides 



valid 
5938459282:
5928292841: 
5938459282:
5928292841: 

4  subtract X from both sides 



LHS diff is pdg1464*(pdg1939 + pdg9139)/pdg9139 RHS diff is 0 
5958392859:
5938459282: 
5958392859:
5938459282: 

9  square root both sides 



no check performed 
9385938295:
5982958249: 9582958294: 
9385938295:
5982958249: 9582958294: 

8  LHS of expr 1 equals LHS of expr 2 



input diff is 0 diff is (pdg1464**2*pdg9139 + pdg1464*pdg1939 + pdg4231)/pdg9139 diff is (pdg1464**2*pdg9139 + pdg1464*pdg1939 + pdg4231)/pdg9139 
5928292841:
5959282914: 9385938295: 
5928292841:
5959282914: 9385938295: 

7  simplify 



valid 
5928285821:
5959282914: 
5928285821:
5959282914: 

6  change variable X to Y 



valid 
8582954722:
dimensions are consistent 5928285821: 
8582954722:
N/A 5928285821: 

14  declare final expr 



no validation is available for declarations 
9999999968:

9999999968:


15  declare final expr 



no validation is available for declarations 
9999999969:

9999999969:


3  divide both sides by 



LHS diff is pdg1464*(pdg1939  pdg9139)/pdg9139 RHS diff is 0 
9285928292:
5958392859: 
9285928292:
5958392859: 

1  declare initial expr 



no validation is available for declarations 
9285928292:

9285928292:


7.5  declare initial expr 



no validation is available for declarations 
8582954722:
dimensions are consistent 
8582954722:
N/A 
symbol ID  category  latex  scope  dimension  name  value  Used in derivations  references  

9139  variable 
a
\(a\) 
['real']  dimensionless  45  
1939  variable 
b
\(b\) 
['real']  dimensionless  20  
1464  variable 
x
\(x\) 
['real']  dimensionless 

140  
3410  variable 
h
\(h\) 
real  dimensionless  none 

2  
4231  variable 
c
\(c\) 
['real']  dimensionless  12 