Use completing the square to solve 10r^2 = 45 - 68r.

Rewrite as

10r^2 + 68r  =  45       divide  through by 10

r^2  + (68/10)r  = 45/10

r^2 + 6.8r   =  4.5         take 1/2  of  6.8 = 3.4  square it = 11.56  add to both sides

{ the number in  red is what we need later }

r^2 + 6.8r + 11.56  =  4.5 + 11.56

(r + 3.4)^2 =  16.06      take both roots

r + 3.4 =   ±√ 16.06

r = √16.06  - 3.4  ≈  .6075 

or

r = - √16.06 - 3.4  ≈ -7.4075