15a^2+5a-3=0

Simple and best practice solution for 15a^2+5a-3=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 15a^2+5a-3=0 equation: 


Simplifying
15a2 + 5a + -3 = 0

Reorder the terms:
-3 + 5a + 15a2 = 0

Solving
-3 + 5a + 15a2 = 0

Solving for variable 'a'.

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

Divide each side by '15'.
-0.2 + 0.3333333333a + a2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.3333333333a + 0.2 + a2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.3333333333a + a2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.3333333333a + a2 = 0 + 0.2
0.3333333333a + a2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.3333333333a + a2 = 0.2

The a term is 0.3333333333a.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333a + 0.02777777779 + a2 = 0.2 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333a + a2 = 0.2 + 0.02777777779

Combine like terms: 0.2 + 0.02777777779 = 0.22777777779
0.02777777779 + 0.3333333333a + a2 = 0.22777777779

Factor a perfect square on the left side:
(a + 0.1666666667)(a + 0.1666666667) = 0.22777777779

Calculate the square root of the right side: 0.477260702

Break this problem into two subproblems by setting 
(a + 0.1666666667) equal to 0.477260702 and -0.477260702.


Subproblem 1
a + 0.1666666667 = 0.477260702

Simplifying
a + 0.1666666667 = 0.477260702

Reorder the terms:
0.1666666667 + a = 0.477260702

Solving
0.1666666667 + a = 0.477260702

Solving for variable 'a'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + a = 0.477260702 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + a = 0.477260702 + -0.1666666667
a = 0.477260702 + -0.1666666667

Combine like terms: 0.477260702 + -0.1666666667 = 0.3105940353
a = 0.3105940353

Simplifying
a = 0.3105940353


Subproblem 2
a + 0.1666666667 = -0.477260702

Simplifying
a + 0.1666666667 = -0.477260702

Reorder the terms:
0.1666666667 + a = -0.477260702

Solving
0.1666666667 + a = -0.477260702

Solving for variable 'a'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + a = -0.477260702 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + a = -0.477260702 + -0.1666666667
a = -0.477260702 + -0.1666666667

Combine like terms: -0.477260702 + -0.1666666667 = -0.6439273687
a = -0.6439273687

Simplifying
a = -0.6439273687


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.3105940353, -0.6439273687}

See similar equations:

| f(-x)=6x^2+7x-6 | | y^2-90=13*y | | 5(x+14)=3(x-11) | | c+48=3c | | 8n-16=5n+35 | | 18a^4b^6/2a^2b^3 | | 15=72+6x | | f(x+1)=6x^2+7x-6 | | s-5=7s-89 | | .3333x-6=.1429x+2 | | n^2-120=7*n | | -4.072=.8b | | 12+c=7 | | 7r+2= | | z+28+z+96=180 | | 5x+14=-3x-33 | | (a^2-5a)/(a^2-4a-5) | | 9x+8=-208 | | 1/15=1/19+1/c | | a+24=7a | | x^3-5x^2+4a=0 | | c+14=8c | | 30/155 | | 13=2(x-1)+1 | | 5(x+14)=-3x-33 | | 8=3(v-4)-8v | | c+14=c | | x^2-3x+1=2-3x | | (5b-9)=(8-2b) | | -4y-3(-7y-3)=-7-8(1-y) | | b^2-2=0 | | 2a+a+36=180 |

Equations solver categories