2x^2=17x-30

Solution for 2x^2=17x-30 equation:

Simplifying
2x2 = 17x + -30

Reorder the terms:
2x2 = -30 + 17x

Solving
2x2 = -30 + 17x

Solving for variable 'x'.

Reorder the terms:
30 + -17x + 2x2 = -30 + 17x + 30 + -17x

Reorder the terms:
30 + -17x + 2x2 = -30 + 30 + 17x + -17x

Combine like terms: -30 + 30 = 0
30 + -17x + 2x2 = 0 + 17x + -17x
30 + -17x + 2x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
30 + -17x + 2x2 = 0

Factor a trinomial.
(5 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {2.5, 6}