2x^2-17x+45=10

Solution for 2x^2-17x+45=10 equation:

Simplifying
2x2 + -17x + 45 = 10

Reorder the terms:
45 + -17x + 2x2 = 10

Solving
45 + -17x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
45 + -10 + -17x + 2x2 = 10 + -10

Combine like terms: 45 + -10 = 35
35 + -17x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
35 + -17x + 2x2 = 0

Factor a trinomial.
(7 + -2x)(5 + -1x) = 0

Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {3.5, 5}