6a^2+9a-5=0

Simple and best practice solution for 6a^2+9a-5=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 6a^2+9a-5=0 equation:


Simplifying
6a2 + 9a + -5 = 0

Reorder the terms:
-5 + 9a + 6a2 = 0

Solving
-5 + 9a + 6a2 = 0

Solving for variable 'a'.

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

Divide each side by '6'.
-0.8333333333 + 1.5a + a2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 1.5a + 0.8333333333 + a2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 1.5a + a2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 1.5a + a2 = 0 + 0.8333333333
1.5a + a2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
1.5a + a2 = 0.8333333333

The a term is 1.5a.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5a + 0.5625 + a2 = 0.8333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = 0.8333333333 + 0.5625

Combine like terms: 0.8333333333 + 0.5625 = 1.3958333333
0.5625 + 1.5a + a2 = 1.3958333333

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = 1.3958333333

Calculate the square root of the right side: 1.181453907

Break this problem into two subproblems by setting 
(a + 0.75) equal to 1.181453907 and -1.181453907.

Subproblem 1

a + 0.75 = 1.181453907 Simplifying a + 0.75 = 1.181453907 Reorder the terms: 0.75 + a = 1.181453907 Solving 0.75 + a = 1.181453907 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = 1.181453907 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 1.181453907 + -0.75 a = 1.181453907 + -0.75 Combine like terms: 1.181453907 + -0.75 = 0.431453907 a = 0.431453907 Simplifying a = 0.431453907

Subproblem 2

a + 0.75 = -1.181453907 Simplifying a + 0.75 = -1.181453907 Reorder the terms: 0.75 + a = -1.181453907 Solving 0.75 + a = -1.181453907 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = -1.181453907 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -1.181453907 + -0.75 a = -1.181453907 + -0.75 Combine like terms: -1.181453907 + -0.75 = -1.931453907 a = -1.931453907 Simplifying a = -1.931453907

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.431453907, -1.931453907}

See similar equations:

| x+120-x=0 | | -48/2*6-4= | | -[2z-(4z+4)]=4+(1z+9) | | 2x-1=5+3x | | -13=5(1+4m)-4m | | 45M^5-44M^2N^3=0 | | e/2.44=0.12/24.4 | | -10+3*2= | | 8=4x-2y | | (4x^3-9x)-(6x^3+8x+3)= | | y=2x^2+8 | | 17=11+n^3 | | 6x^2-61x+63=0 | | 3x-10+x=9 | | 3(x+8)=8 | | 4a^15/4a^9 | | x-.25x-7.00=65.00 | | 12x+2=3x+5 | | 3x-13+2x-4+64=180 | | d^2+13d+40=0 | | 12=z+4 | | 3cosx=y | | 196=4x+4[7x+9] | | (-2+-1x)(16+-7x)=0 | | 6x+74+5x-48=180 | | 4x+8-6x-4=60 | | 3x-13+2x-4=180 | | 45M^5-44M^2N^3-6M^2+44N^2=0 | | 3x^2-x=162 | | 9x-5+3x+7=134 | | Ifln(3x+5)=2 | | (x-0)(x-8)=0 |

Equations solver categories