Question

Solve the equation for x, where x is a real number:
-5x^2 + 4x - 3 = 0

Answer 1

We can find solutions analytically by applying the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -4 ± √((4)^2 - 4(-5)(-3)) ] / ( 2(-5) )
x = [-4 ± √(16 - (60) ) ] / ( -10 )
x = [-4 ± √(-44) ] / ( -10)
√(-44) is nonreal, so the answer to this question is that there are no real solutions.

Answer 2

The equation has no real solutions. (The graph has no x-intercepts.)

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The complex solutions are x = 0.4 ±i√0.44.