3x^2-5x=4

Simple and best practice solution for 3x^2-5x=4 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^2-5x=4 equation: 


Simplifying
3x2 + -5x = 4

Reorder the terms:
-5x + 3x2 = 4

Solving
-5x + 3x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -5x + 3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -5x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -1.666666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -1.666666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + 1.333333333
-1.666666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-1.666666667x + x2 = 1.333333333

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 1.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 1.333333333 + 0.6944444447

Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777
0.6944444447 + -1.666666667x + x2 = 2.0277777777

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 2.0277777777

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.424000624 and -1.424000624.


Subproblem 1
x + -0.8333333335 = 1.424000624

Simplifying
x + -0.8333333335 = 1.424000624

Reorder the terms:
-0.8333333335 + x = 1.424000624

Solving
-0.8333333335 + x = 1.424000624

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 1.424000624 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 1.424000624 + 0.8333333335
x = 1.424000624 + 0.8333333335

Combine like terms: 1.424000624 + 0.8333333335 = 2.2573339575
x = 2.2573339575

Simplifying
x = 2.2573339575


Subproblem 2
x + -0.8333333335 = -1.424000624

Simplifying
x + -0.8333333335 = -1.424000624

Reorder the terms:
-0.8333333335 + x = -1.424000624

Solving
-0.8333333335 + x = -1.424000624

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -1.424000624 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -1.424000624 + 0.8333333335
x = -1.424000624 + 0.8333333335

Combine like terms: -1.424000624 + 0.8333333335 = -0.5906672905
x = -0.5906672905

Simplifying
x = -0.5906672905


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2573339575, -0.5906672905}

See similar equations:

| 3m^2=7m+6 | | -2.06d+26.8=50.72 | | 4x+y=700 | | x+70=650 | | (x)=-4x+16 | | x+140=2760 | | 20=-8v+4(v+4) | | x+x+2=88 | | 1x-3y=6 | | x+x+2=52 | | 2x+7=x+15 | | x+x+2=114 | | x+x+2=14 | | x+x+2=66 | | 3x^4-27x^2=0 | | 5.05x(3.075)= | | -1x(3)= | | 16a+16b= | | -31x(6.75)= | | 8x^2-27x-20=0 | | -5x(-3)= | | 4.7x(-2.3)= | | 5t+10-5= | | 47.3x(-5.2)= | | 8x(-6)= | | -103x(-23)= | | 7t^2=0 | | -(3y+2)-(-2y-7)=4 | | 4(4x-2)=2(8x+9) | | 8+2m-6=8m+11-5m | | -3x+8=41 | | 9s+9s=108 |

Equations solver categories