Actually, this is easier than you think.  You can solve the 3^2=9  then it's 9-1 +4x=0

8+4x=0  becomes 4x=-8;  x=-2.  no factoring needed!

don't know if you have a typo, but first I solve it the way you wrote it and then I solve it considerting that in stead for ^2 you meant to write x^2:

3^2 + 4x -1 = 0

9 + 4X - 1 = 0    add 9 and -1

4x +8 = 0   add -8 on both sides

4x + 8 -8 = -8

4x +0 = -8

4x = -8  dived both sides by 4

4x/4 = -

x = -2

now solve:

3x^2 + 4x -1 = 0    use formula x_1.2= (-b +/-  sqrt( b²- 4ac ) / 2a   ,   considering  x² +bx +c = 0

x_1,2 = ( -4 +/- sqrt(16 - 4*3*(-1) ) / 2*3

x1,2 = ( -4 +/- sqrt(28) ) / 6

x_1,2 = ( -4 +/- 2sqrt7) /6