6x^2+14x-30=0

Simple and best practice solution for 6x^2+14x-30=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+14x-30=0 equation: 


Simplifying
6x2 + 14x + -30 = 0

Reorder the terms:
-30 + 14x + 6x2 = 0

Solving
-30 + 14x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 7x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 7x + 3x2)' equal to zero and attempt to solve:

Simplifying
-15 + 7x + 3x2 = 0

Solving
-15 + 7x + 3x2 = 0

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

Divide each side by '3'.
-5 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 2.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2.333333333x + x2 = 0 + 5
2.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
2.333333333x + x2 = 5

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 5 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 5 + 1.361111112

Combine like terms: 5 + 1.361111112 = 6.361111112
1.361111112 + 2.333333333x + x2 = 6.361111112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 6.361111112

Calculate the square root of the right side: 2.522124325

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 2.522124325 and -2.522124325.


Subproblem 1
x + 1.166666667 = 2.522124325

Simplifying
x + 1.166666667 = 2.522124325

Reorder the terms:
1.166666667 + x = 2.522124325

Solving
1.166666667 + x = 2.522124325

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 2.522124325 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 2.522124325 + -1.166666667
x = 2.522124325 + -1.166666667

Combine like terms: 2.522124325 + -1.166666667 = 1.355457658
x = 1.355457658

Simplifying
x = 1.355457658


Subproblem 2
x + 1.166666667 = -2.522124325

Simplifying
x + 1.166666667 = -2.522124325

Reorder the terms:
1.166666667 + x = -2.522124325

Solving
1.166666667 + x = -2.522124325

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -2.522124325 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -2.522124325 + -1.166666667
x = -2.522124325 + -1.166666667

Combine like terms: -2.522124325 + -1.166666667 = -3.688790992
x = -3.688790992

Simplifying
x = -3.688790992


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.355457658, -3.688790992}
Solution
x = {1.355457658, -3.688790992}

See similar equations:

| 2/7f=5/7 | | X/2=0.6 | | 525+.21c=585+.13c | | 2c+10+c+10+c=107 | | x+1(x-4)=x-5(x+4) | | y=-5/7x5-5 | | 5x+10x-7x-5= | | 2(8x+1)=5(3x+1) | | 6x^2-16x-30=0 | | -400x+4000=2400 | | a-5-(-2)=7-q | | -3/10p=3/10 | | 3x=195 | | Y-26=34 | | 4a-9a+3=-32 | | -356=7(z-8) | | 7/3x=21 | | 4a+9a+3=-32 | | 10x-14xy= | | 13*17/1/3 | | 8/14z=6/8 | | 3.14=c/d | | -8+x+6x=-34 | | -17=3a-8 | | Y-6=-1 | | 4.5(3)+4.5x=24.75 | | 7(n+5)+3(n-1)= | | a+9-2a=6 | | 8(r+7)=56 | | -5x+40=6-70 | | 1/10h=9/5 | | 2(n+7)+5(n+8)= |

Equations solver categories