Find the solutions of the quadratic equation 7x^2-2x+3=0.

x = 1/7 + (2 i sqrt (5)) / 7 or x = 1/7 - (2 i sqrt (5)) / 7

Step-by-step explanation:

Solve for x:

7 x^2 - 2 x + 3 = 0

Divide both sides by 7:

x^2 - (2 x) / 7 + 3/7 = 0

Subtract 3/7 from both sides:

x^2 - (2 x) / 7 = - 3/7

Add 1/49 to both sides:

x^2 - (2 x) / 7 + 1/49 = - 20/49

Write the left hand side as a square:

(x - 1/7) ^2 = - 20/49

Take the square root of both sides:

x - 1/7 = (2 i sqrt (5)) / 7 or x - 1/7 = - (2 i sqrt (5)) / 7

Add 1/7 to both sides:

x = 1/7 + (2 i sqrt (5)) / 7 or x - 1/7 = - (2 i sqrt (5)) / 7

Add 1/7 to both sides:

Answer: x = 1/7 + (2 i sqrt (5)) / 7 or x = 1/7 - (2 i sqrt (5)) / 7