Solving quadratic equations by completing the square

3 x^2 + 12 x - 5 = 0
3 ( x^2 + 4 x - 5/3) = 0
x^2 + 4 x - 5/3 =0
( x + 2)^2 - 4 - 5/3 = 0
(x+2)^2 - 17/3 = 0
(x+2)^2 = 17/3

x + 2 = sqrt(17/3) or x+ 2 = -sqrt(17/3)

x = - 2 +- sqrt(17/3)
= 1/3 ( -6 +- sqrt(51) )

P(x) = 3x² + 12x - 5 = 0
=> x² + 4x - 5/3 = 0
=> x² + 4x + 4 = 5/3 + 4
=> (x + 2)² = 17/3
=> x + 2 = ±√(17/3)
=> x = -2 ± √(17/3)
=> x = -2 ± √(17*3/(3*3))
=> x = -2 ± (√51)/3
=> x = [-6 ± (√51)]/3

3 (x ² + 4x) = 5/3

3 ( x ² + 4x + 4) = 5/3 + 12

3 (x + 2) ² = 41/3

(x + 2)² = 41/9

x + 2 = ± √41 / 3

x = - 2 ± √41 / 3

x = [ - 6 ± √41 ] / 3