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:

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