Use the discriminant to determine how many solutions are possible for the following equation showwork)5x^2-3x+4=0​

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