7x^2+8x-6=

Solution for 7x^2+8x-6= equation:

Simplifying
7x2 + 8x + -6 = 0

Reorder the terms:
-6 + 8x + 7x2 = 0

Solving
-6 + 8x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-0.8571428571 + 1.142857143x + x2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + 1.142857143x + 0.8571428571 + x2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + 1.142857143x + x2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + 1.142857143x + x2 = 0 + 0.8571428571
1.142857143x + x2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
1.142857143x + x2 = 0.8571428571

The x term is 1.142857143x.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143x + 0.3265306123 + x2 = 0.8571428571 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143x + x2 = 0.8571428571 + 0.3265306123

Combine like terms: 0.8571428571 + 0.3265306123 = 1.1836734694
0.3265306123 + 1.142857143x + x2 = 1.1836734694

Factor a perfect square on the left side:
(x + 0.5714285715)(x + 0.5714285715) = 1.1836734694

Calculate the square root of the right side: 1.087967587

Break this problem into two subproblems by setting 
(x + 0.5714285715) equal to 1.087967587 and -1.087967587.

Subproblem 1
x + 0.5714285715 = 1.087967587

Simplifying
x + 0.5714285715 = 1.087967587

Reorder the terms:
0.5714285715 + x = 1.087967587

Solving
0.5714285715 + x = 1.087967587

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x = 1.087967587 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x = 1.087967587 + -0.5714285715
x = 1.087967587 + -0.5714285715

Combine like terms: 1.087967587 + -0.5714285715 = 0.5165390155
x = 0.5165390155

Simplifying
x = 0.5165390155

Subproblem 2
x + 0.5714285715 = -1.087967587

Simplifying
x + 0.5714285715 = -1.087967587

Reorder the terms:
0.5714285715 + x = -1.087967587

Solving
0.5714285715 + x = -1.087967587

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x = -1.087967587 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x = -1.087967587 + -0.5714285715
x = -1.087967587 + -0.5714285715

Combine like terms: -1.087967587 + -0.5714285715 = -1.6593961585
x = -1.6593961585

Simplifying
x = -1.6593961585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5165390155, -1.6593961585}