5r^2-17r+14=0

Solution for 5r^2-17r+14=0 equation:

Simplifying
5r2 + -17r + 14 = 0

Reorder the terms:
14 + -17r + 5r2 = 0

Solving
14 + -17r + 5r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(7 + -5r)' equal to zero and attempt to solve:

Simplifying
7 + -5r = 0

Solving
7 + -5r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5r = 0 + -7
-5r = 0 + -7

Combine like terms: 0 + -7 = -7
-5r = -7

Divide each side by '-5'.
r = 1.4

Simplifying
r = 1.4
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {1.4, 2}