6x^2=7x+9

Simple and best practice solution for 6x^2=7x+9 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=7x+9 equation:


Simplifying
6x2 = 7x + 9

Reorder the terms:
6x2 = 9 + 7x

Solving
6x2 = 9 + 7x

Solving for variable 'x'.

Reorder the terms:
-9 + -7x + 6x2 = 9 + 7x + -9 + -7x

Reorder the terms:
-9 + -7x + 6x2 = 9 + -9 + 7x + -7x

Combine like terms: 9 + -9 = 0
-9 + -7x + 6x2 = 0 + 7x + -7x
-9 + -7x + 6x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-9 + -7x + 6x2 = 0

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

Divide each side by '6'.
-1.5 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1.166666667x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1.166666667x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1.166666667x + x2 = 0 + 1.5
-1.166666667x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1.166666667x + x2 = 1.5

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = 1.5 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 1.5 + 0.3402777780

Combine like terms: 1.5 + 0.3402777780 = 1.840277778
0.3402777780 + -1.166666667x + x2 = 1.840277778

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 1.840277778

Calculate the square root of the right side: 1.356568383

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 1.356568383 and -1.356568383.

Subproblem 1

x + -0.5833333335 = 1.356568383 Simplifying x + -0.5833333335 = 1.356568383 Reorder the terms: -0.5833333335 + x = 1.356568383 Solving -0.5833333335 + x = 1.356568383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 1.356568383 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.356568383 + 0.5833333335 x = 1.356568383 + 0.5833333335 Combine like terms: 1.356568383 + 0.5833333335 = 1.9399017165 x = 1.9399017165 Simplifying x = 1.9399017165

Subproblem 2

x + -0.5833333335 = -1.356568383 Simplifying x + -0.5833333335 = -1.356568383 Reorder the terms: -0.5833333335 + x = -1.356568383 Solving -0.5833333335 + x = -1.356568383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -1.356568383 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.356568383 + 0.5833333335 x = -1.356568383 + 0.5833333335 Combine like terms: -1.356568383 + 0.5833333335 = -0.7732350495 x = -0.7732350495 Simplifying x = -0.7732350495

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.9399017165, -0.7732350495}

See similar equations:

| 30p^2-99p+27=0 | | 110-4x=41x+15 | | 6-7x=57-28x | | 6-7x=57-28 | | 6(2z-1)-3(z+4)=7(z+1) | | 490=5t^2 | | h(t)=13t | | 3r^2-168=-3r | | 13x^2+5x-125=-2x^2 | | 3x+9y=90 | | x+(x+2)=36 | | 12x+9y=198 | | 150b=-35b^2+25 | | x^2+5x=90 | | 4t+18=14 | | 3n^2=4-11n | | 24x+56=30x-140 | | 18x^2+6x=0 | | 2n^2=16+14 | | y=3x^2+320 | | p=b+4a+3c | | 3Y+4=7y-20 | | 3m^2=15-12m | | 16x+4=21x-21 | | 3x+48=8x+8 | | 3-4x+2=13 | | 2x+4=3x-3 | | 5x+35=-3x+24 | | 8x-5=4x-4 | | 49y^2=81 | | y=3x^2-12x+7 | | x^2-44+c= |

Equations solver categories