6x^2=17x+3

Solution for 6x^2=17x+3 equation:

Simplifying
6x2 = 17x + 3

Reorder the terms:
6x2 = 3 + 17x

Solving
6x2 = 3 + 17x

Solving for variable 'x'.

Reorder the terms:
-3 + -17x + 6x2 = 3 + 17x + -3 + -17x

Reorder the terms:
-3 + -17x + 6x2 = 3 + -3 + 17x + -17x

Combine like terms: 3 + -3 = 0
-3 + -17x + 6x2 = 0 + 17x + -17x
-3 + -17x + 6x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
-3 + -17x + 6x2 = 0

Factor a trinomial.
(-1 + -6x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x = 0 + 1
-6x = 0 + 1

Combine like terms: 0 + 1 = 1
-6x = 1

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.1666666667, 3}