Question

(-3x^2+4x-2)/(-3x+19)

Answer 1

\left[x _{1}\right] = \left[ \frac{2}{3}+\left( \frac{-1}{3}\,i \right) \,\sqrt{2}\right][x​1​​]=[​3​​2​​+(​3​​−1​​i)√​2​​​] totally answer

Answer 2

solve for x: by completing the square:

(3 x^2 - 4 x + 2)/(3 x - 19) = 0

Multiply both sides by 3 x - 19:

3 x^2 - 4 x + 2 = 0

Divide both sides by 3:

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

Subtract 2/3 from both sides:

x^2 - (4 x)/3 = -2/3

Add 4/9 to both sides:

x^2 - (4 x)/3 + 4/9 = -2/9

Write the left hand side as a square:

(x - 2/3)^2 = -2/9

Take the square root of both sides:

x - 2/3 = (i sqrt(2))/3 or x - 2/3 = -(i sqrt(2))/3

Add 2/3 to both sides:

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

Add 2/3 to both sides:

Answer: x = 2/3 + (i sqrt(2))/3 or x = 2/3 - (i sqrt(2))/3