3x^2+17x+6=0

Simple and best practice solution for 3x^2+17x+6=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 3x^2+17x+6=0 equation: 


Simplifying
3x2 + 17x + 6 = 0

Reorder the terms:
6 + 17x + 3x2 = 0

Solving
6 + 17x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
2 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5.666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 5.666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5.666666667x + x2 = 0 + -2
5.666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
5.666666667x + x2 = -2

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = -2 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -2 + 8.027777782

Combine like terms: -2 + 8.027777782 = 6.027777782
8.027777782 + 5.666666667x + x2 = 6.027777782

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 6.027777782

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 2.455153311 and -2.455153311.


Subproblem 1
x + 2.833333334 = 2.455153311

Simplifying
x + 2.833333334 = 2.455153311

Reorder the terms:
2.833333334 + x = 2.455153311

Solving
2.833333334 + x = 2.455153311

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = 2.455153311 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 2.455153311 + -2.833333334
x = 2.455153311 + -2.833333334

Combine like terms: 2.455153311 + -2.833333334 = -0.378180023
x = -0.378180023

Simplifying
x = -0.378180023


Subproblem 2
x + 2.833333334 = -2.455153311

Simplifying
x + 2.833333334 = -2.455153311

Reorder the terms:
2.833333334 + x = -2.455153311

Solving
2.833333334 + x = -2.455153311

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = -2.455153311 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -2.455153311 + -2.833333334
x = -2.455153311 + -2.833333334

Combine like terms: -2.455153311 + -2.833333334 = -5.288486645
x = -5.288486645

Simplifying
x = -5.288486645


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.378180023, -5.288486645}

See similar equations:

| 1/4(1/2+x)=1/2(x/3-3) | | -2(n-1)-5n=2(n-5)-6n | | 2(n+7)=4-2(n-5) | | F(h)=3.5h+500 | | x/-7=9 | | 4(-3c+1)=-10(c-4)-14c | | x(2x-5)=(2x+9)(x-4) | | -2(1-2b)+3b=2(4+4b) | | 64x^2-49y^2=0 | | x^19/2 | | 4x-2x+8x=30 | | (231/2)/(41/5) | | 10g+15=7g | | 5+5+6=151872 | | 3x+5-x=4x-4-7 | | 12m+8m=9(4m-12)-4(m+6) | | -06+0.05x=5.3 | | -14=n+4-4n | | 13b+12c= | | 2r^2-9r-5=0 | | 153=(x+x+2+x+4) | | 1/2-x/12=7/12 | | 5m^2-22m+17=0 | | 60=8x | | -2y+9=23 | | 2a^3-3a^2+8=0 | | 8n-(5n+4)=2 | | 10x+10=11x-1 | | 8x13+42/18-6+5 | | 16x-2=110 | | 3n-(12+8n)=-5n-2(n+6) | | 2x^2-14x-13=0 |

Equations solver categories