We can use the quadratic formula to solve this.
3x^2 - x- 1 = 0
ax^2 + bx + c = 0
a = 3
b = -1
c = -1
x = (-b +- sqrt(b^2-4ac)) / (2a)
x = (-(-1) +- sqrt(-1^2-4 xx 3 xx -1)) / (2 xx 6)
x = (1 +- sqrt( 1 - 12 xx -1)) / (2 xx 6)
x = (1 +- sqrt( 1 - -12)) / 12
x = (1 +- sqrt13) / 12
x = (1 +- 3.605551275) / 12
x_1 = (1 + 3.605551275) / 12
x_1 = (4.605551275) / 12
color(blue)( x_1 = 0.3837959396 or (1 + sqrt13) / 12
x_2 = (1 - 3.605551275) / 12
x_2 = -2.605551275 / 12
color(blue)( x_2 = -0.217129273 or (1 - sqrt13) / 12