Use the discriminant to determine how many solutions are possible for the following equation show

work)

5x^2-3x+4=0

x = 3/10 + (i sqrt (71)) / 10 or x = 3/10 - (i sqrt (71)) / 10

Step-by-step explanation:

Solve for x:

5 x^2 - 3 x + 4 = 0

Divide both sides by 5:

x^2 - (3 x) / 5 + 4/5 = 0

Subtract 4/5 from both sides:

x^2 - (3 x) / 5 = - 4/5

Add 9/100 to both sides:

x^2 - (3 x) / 5 + 9/100 = - 71/100

Write the left hand side as a square:

(x - 3/10) ^2 = - 71/100

Take the square root of both sides:

x - 3/10 = (i sqrt (71)) / 10 or x - 3/10 = - (i sqrt (71)) / 10

Add 3/10 to both sides:

x = 3/10 + (i sqrt (71)) / 10 or x - 3/10 = - (i sqrt (71)) / 10

Add 3/10 to both sides:

Answer: x = 3/10 + (i sqrt (71)) / 10 or x = 3/10 - (i sqrt (71)) / 10