5p^2+10p-3=0

Solution for 5p^2+10p-3=0 equation:

Simplifying
5p2 + 10p + -3 = 0

Reorder the terms:
-3 + 10p + 5p2 = 0

Solving
-3 + 10p + 5p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.6 + 2p + p2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 2p + 0.6 + p2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 2p + p2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 2p + p2 = 0 + 0.6
2p + p2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
2p + p2 = 0.6

The p term is 2p.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2p + 1 + p2 = 0.6 + 1

Reorder the terms:
1 + 2p + p2 = 0.6 + 1

Combine like terms: 0.6 + 1 = 1.6
1 + 2p + p2 = 1.6

Factor a perfect square on the left side:
(p + 1)(p + 1) = 1.6

Calculate the square root of the right side: 1.264911064

Break this problem into two subproblems by setting 
(p + 1) equal to 1.264911064 and -1.264911064.

Subproblem 1
p + 1 = 1.264911064

Simplifying
p + 1 = 1.264911064

Reorder the terms:
1 + p = 1.264911064

Solving
1 + p = 1.264911064

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + p = 1.264911064 + -1

Combine like terms: 1 + -1 = 0
0 + p = 1.264911064 + -1
p = 1.264911064 + -1

Combine like terms: 1.264911064 + -1 = 0.264911064
p = 0.264911064

Simplifying
p = 0.264911064

Subproblem 2
p + 1 = -1.264911064

Simplifying
p + 1 = -1.264911064

Reorder the terms:
1 + p = -1.264911064

Solving
1 + p = -1.264911064

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + p = -1.264911064 + -1

Combine like terms: 1 + -1 = 0
0 + p = -1.264911064 + -1
p = -1.264911064 + -1

Combine like terms: -1.264911064 + -1 = -2.264911064
p = -2.264911064

Simplifying
p = -2.264911064

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.264911064, -2.264911064}