# Solving Equations

## Solving Equations

SymPy's `solve()`

function can be used to solve equations and expressions that contain symbolic math variables.

### Equations with one solution

A simple equation that contains one variable like x-4-2 = 0 can be solved using the solve function. When only one value is part of the solution, the solution is in the form of a list.

The code section below demonstrates SymPy's `solve()`

function when an expression is defined with symbolic math variables.

```
from sympy import symbols, solve
```x = symbols('x')
expr = x-4-2

sol = solve(expr)

sol

```
num = sol[0]
```num

```
from sympy import symbols, Eq, solve
```y = symbols('y')
eq1 = Eq(y + 3 + 8)

sol = solve(eq1)
sol

### Equations with two solutions

Quadratic equations, like x^2 - 5x + 6 = 0, have two solutions. SymPy's `solve()`

function can be used to solve an equation with two solutions. When an equation has two solutions, SymPy outputs a list. The elements in the list are the two solutions.

The code section below shows how SymPy's `solve()`

function solves an equation with two solutions.

```
from sympy import symbols, Eq, solve
```y = symbols('x')
eq1 = Eq(x**2 -5*x + 6)

sol = solve(eq1)
sol

`dict=True`

to SymPy's `solve()`

function, the output is still a list, but inside the list is a dictionary that shows which variable was solved for.
```
from sympy import symbols, Eq, solve
```y = symbols('x')
eq1 = Eq(x**2 -5*x + 6)

sol = solve(eq1, dict=True)
sol

```
sol[0]
```

```
sol[1]
```