To solve the equation 5x^2 - 2x + 3 = 0, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
Substituting the given values, we get:
x = (-(-2) ± sqrt((-2)^2 - 4(5)(3))) / 2(5)
x = (2 ± sqrt(4 - 60)) / 10
x = (2 ± sqrt(-56)) / 10
The expression under the square root is negative, which means that the equation has no real solutions. The solutions are complex numbers.
Therefore, the solution to the equation 5x^2 - 2x + 3 = 0 is:
x = (2 ± i*sqrt(56)) / 10, where i is the imaginary unit.