5r^2-34r+45=0

Solution for 5r^2-34r+45=0 equation:

Simplifying
5r2 + -34r + 45 = 0

Reorder the terms:
45 + -34r + 5r2 = 0

Solving
45 + -34r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(9 + -5r)(5 + -1r) = 0

Subproblem 1
Set the factor '(9 + -5r)' equal to zero and attempt to solve:

Simplifying
9 + -5r = 0

Solving
9 + -5r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5r = 0 + -9
-5r = 0 + -9

Combine like terms: 0 + -9 = -9
-5r = -9

Divide each side by '-5'.
r = 1.8

Simplifying
r = 1.8
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

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

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

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

Simplifying
r = 5
Solution
r = {1.8, 5}