y^2+3y-24=0

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Solution for y^2+3y-24=0 equation:


Simplifying
y2 + 3y + -24 = 0

Reorder the terms:
-24 + 3y + y2 = 0

Solving
-24 + 3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 3y + 24 + y2 = 0 + 24

Reorder the terms:
-24 + 24 + 3y + y2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 3y + y2 = 0 + 24
3y + y2 = 0 + 24

Combine like terms: 0 + 24 = 24
3y + y2 = 24

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 24 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 24 + 2.25

Combine like terms: 24 + 2.25 = 26.25
2.25 + 3y + y2 = 26.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(y + 1.5) equal to 5.123475383 and -5.123475383.

Subproblem 1

y + 1.5 = 5.123475383 Simplifying y + 1.5 = 5.123475383 Reorder the terms: 1.5 + y = 5.123475383 Solving 1.5 + y = 5.123475383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 5.123475383 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 5.123475383 + -1.5 y = 5.123475383 + -1.5 Combine like terms: 5.123475383 + -1.5 = 3.623475383 y = 3.623475383 Simplifying y = 3.623475383

Subproblem 2

y + 1.5 = -5.123475383 Simplifying y + 1.5 = -5.123475383 Reorder the terms: 1.5 + y = -5.123475383 Solving 1.5 + y = -5.123475383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -5.123475383 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -5.123475383 + -1.5 y = -5.123475383 + -1.5 Combine like terms: -5.123475383 + -1.5 = -6.623475383 y = -6.623475383 Simplifying y = -6.623475383

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.623475383, -6.623475383}

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