18x^2 - 27x + 4 = 0
To find solutions for this equation you need to first factorise it.
So you need to think about the multiples of 18 and 4.
Multiples of 18 are: 1x18, 2x9, 3x6,
And multiples of 4 are: 1x4, 2x2,
You now need to think about which multiples to use that would work to get your equation:
In this case 6x3 and 4x1 work to get your equation, however, because the 27 is negative, the solution is:
18x^2 - 27 + 4 = (6x - 1)(3x - 4)
You can then check that this answer is true by multiplying out:
(6x - 1)(3x - 4) = 18x^2 - 24x - 3x - (-4) = 18x^2 - 27x + 4
Which is correct.
So now we know that,
18x^2 - 27x + 4 = (6x - 1)(3x - 4) = 0
So the solutions are,
6x - 1 = 0 and 3x - 4 = 0
6x = 1 and 3x = 4
x = 1/6 and x = 4/3