6x^2+17x-51=0

Simple and best practice solution for 6x^2+17x-51=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 6x^2+17x-51=0 equation:


Simplifying
6x2 + 17x + -51 = 0

Reorder the terms:
-51 + 17x + 6x2 = 0

Solving
-51 + 17x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-8.5 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 2.833333333x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 2.833333333x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 2.833333333x + x2 = 0 + 8.5
2.833333333x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
2.833333333x + x2 = 8.5

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = 8.5 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = 8.5 + 2.006944445

Combine like terms: 8.5 + 2.006944445 = 10.506944445
2.006944445 + 2.833333333x + x2 = 10.506944445

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = 10.506944445

Calculate the square root of the right side: 3.241441723

Break this problem into two subproblems by setting 
(x + 1.416666667) equal to 3.241441723 and -3.241441723.

Subproblem 1

x + 1.416666667 = 3.241441723 Simplifying x + 1.416666667 = 3.241441723 Reorder the terms: 1.416666667 + x = 3.241441723 Solving 1.416666667 + x = 3.241441723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = 3.241441723 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = 3.241441723 + -1.416666667 x = 3.241441723 + -1.416666667 Combine like terms: 3.241441723 + -1.416666667 = 1.824775056 x = 1.824775056 Simplifying x = 1.824775056

Subproblem 2

x + 1.416666667 = -3.241441723 Simplifying x + 1.416666667 = -3.241441723 Reorder the terms: 1.416666667 + x = -3.241441723 Solving 1.416666667 + x = -3.241441723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = -3.241441723 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = -3.241441723 + -1.416666667 x = -3.241441723 + -1.416666667 Combine like terms: -3.241441723 + -1.416666667 = -4.65810839 x = -4.65810839 Simplifying x = -4.65810839

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.824775056, -4.65810839}

See similar equations:

| 7k+15=15k+35 | | 8y-2-6y+1= | | (2x-3y+1)dx=-(6x+4y-3)dy | | 0=5-3lnx | | d/dx(ln(2/sinx)) | | ln(2/sinx) | | 2(2x+8)=5x | | 5/6(x=4)=2x-5 | | 0.04p+0.08(1600-p)=75 | | 5/6(x-4) | | 12y^2+14y+4= | | 8/9-3/10 | | 8a+5a-7a= | | 2(0.3x-9)=5+x | | 8.6y+3.4=4.2-9.8 | | 5x+88=2x+141 | | 150x+3000=30000 | | 8x+66=2x+120 | | 5/6x+2/9=1/3 | | 8x+35=3x+85 | | x^3+12x^2-21x+10=0 | | ln(x+36)=4 | | 4(3a+1)=8 | | 2x-7=48-3x | | sqrt(4a-4)= | | 1-x/(2x-x*x)=1/6 | | 2n-8=90 | | 2x+6x+4x+4x-6+2x-16+6x+2=540 | | 2n-168=180 | | 1-x/2x-x*x=1/6 | | (1+x-2x^3)=0 | | 2n+64=90 |

Equations solver categories