Solve the following equation by completeing the square 3x2

Solve the following equation by completeing the square

3x² + x -1/6 = 0

Find the real solutions of the following equation using the quadratic formula.

x² - 6x -5= 0

1) 3x^2 + x -1/6

Divide by 3 :

x^2 + x/3 -1/2 =0

x^2 +x/3 + (1/6)^2 - ( 1/6)^2 -1/2 =0

( x +1/6)^2 - 1/36 -1/2 =0

(x+1/6)^2 = ( 1+18)/36

So, taking square root on both sides:

(x+1/6 = + / - sqrt(19)/6

x = -1/6 + / - sqrt(19)/6 ( Roots of solution)

2) x^2 -6x -5 =0

Using quadratic equation formula:

x = ( -b + /- sqrt( b^2 -4ac)/2a

= ( 6 + /- sqrt( 36 - (-4)*1*(-5) )/2

= ( 6 + /- sqrt(56)/2

x = 3 + / - sqrt14) ( Solution)