6x^2+2x-3=0

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


Simplifying
6x2 + 2x + -3 = 0

Reorder the terms:
-3 + 2x + 6x2 = 0

Solving
-3 + 2x + 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'.
-0.5 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.3333333333x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.3333333333x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.3333333333x + x2 = 0 + 0.5
0.3333333333x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.3333333333x + x2 = 0.5

The x term is 0.3333333333x.  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.
0.3333333333x + 0.02777777779 + x2 = 0.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.5 + 0.02777777779

Combine like terms: 0.5 + 0.02777777779 = 0.52777777779
0.02777777779 + 0.3333333333x + x2 = 0.52777777779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.52777777779

Calculate the square root of the right side: 0.726483157

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.726483157 and -0.726483157.


Subproblem 1
x + 0.1666666667 = 0.726483157

Simplifying
x + 0.1666666667 = 0.726483157

Reorder the terms:
0.1666666667 + x = 0.726483157

Solving
0.1666666667 + x = 0.726483157

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 0.726483157 + -0.1666666667
x = 0.726483157 + -0.1666666667

Combine like terms: 0.726483157 + -0.1666666667 = 0.5598164903
x = 0.5598164903

Simplifying
x = 0.5598164903


Subproblem 2
x + 0.1666666667 = -0.726483157

Simplifying
x + 0.1666666667 = -0.726483157

Reorder the terms:
0.1666666667 + x = -0.726483157

Solving
0.1666666667 + x = -0.726483157

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -0.726483157 + -0.1666666667
x = -0.726483157 + -0.1666666667

Combine like terms: -0.726483157 + -0.1666666667 = -0.8931498237
x = -0.8931498237

Simplifying
x = -0.8931498237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5598164903, -0.8931498237}

See similar equations:

| 8x+80+7x=50 | | h^2-19h=-90 | | -5=n(n-6) | | q^3=36q | | 2z(z+3)+15=3(z^2-6)-2z | | (p-4)(p-1)=18 | | q^2-8q=33 | | 798*76+90-54=543-8+904 | | 30=z(z-7) | | t^3=49t | | 8y^2=6 | | 12+y=27 | | 52x+26=90x-240 | | 7z(8z+9)(z-9)=0 | | 0=5ln(x+0.5) | | 5k(k+1)+5=6(k^2+9)+19k | | 5(x+2)-3(x-1)=12(2x-4) | | 10=0.8t+1.8 | | (n+7)(n-1)=48 | | 3a^2+10a+8= | | 10x+20=x+8 | | 1=2a(3.14) | | 10x+2=x+8 | | x^4=2400 | | -15x^2+75x+10=70 | | -15x^2+75x+10=0 | | -15x+75x+10=0 | | -4x+4=21+12x | | 3xt+4=5xt | | 2x+9=101 | | x^2+18x+81=307 | | 7x+3(8)= |

Equations solver categories