What is the answer to this math quadratic equation?

5x^2 -12x + 10 = x^2 +10x
=> 4x^2 - 22x + 10 = 0
=> 2x^2 - 11x + 5 = 0
=> 2x^2 - x - 10x + 5 = 0
=> x(2x -1) - 5(2x - 1) = 0
=> (x - 5)(2x - 1) = 0
x = 5 or 1/2

Question Number 1 :
For this equation 5*x^2 - 12*x + 10 = x^2 + 10*x  , answer the following questions :
 A. Find the roots using Quadratic Formula !

Answer Number 1 :
First, we have to turn equation : 5*x^2 - 12*x + 10 = x^2 + 10*x  , into a*x^2+b*x+c=0 form.
 5*x^2 - 12*x + 10 = x^2 + 10*x  , move everything in the right hand side, to the left hand side of the equation
 <=> 5*x^2 - 12*x + 10 - ( x^2 + 10*x  ) = 0 , which is the same with<=> 5*x^2 - 12*x + 10 + ( -x^2 - 10*x  ) =0 , now open the bracket and we get<=> 4*x^2 - 22*x + 10 = 0

The equation 4*x^2 - 22*x + 10 = 0 is already in a*x^2+b*x+c=0 form.
In that form, we can easily derive that the value of a = 4, b = -22, c = 10.

1A. Find the roots using Quadratic Formula !
  Use the formula,
    x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
  We had know that a = 4, b = -22 and c = 10,
  then the value a,b and c in the abc formula, can be subtituted.
  So x1 = (-(-22) + sqrt( (-22)^2 - 4 * (4)*(10)))/(2*4) and x2 = (-(-22) - sqrt( (-22)^2 - 4 * (4)*(10)))/(2*4)
  Which is the same with x1 = ( 22 + sqrt( 484-160))/(8) and x2 = ( 22 - sqrt( 484-160))/(8)
  Which make x1 = ( 22 + sqrt( 324))/(8) and x2 = ( 22 - sqrt( 324))/(8)
  So we get x1 = ( 22 + 18 )/(8) and x2 = ( 22 - 18 )/(8)
  So we got the answers as x1 = 5 and x2 = 0.5