solve the equation

Question

3x^2-4x+5=0

Answer 1

The Quadratic Equation

3x^2 - 4x + 5  =  0

Compare it to quadratic form ax^2 + bx + c  =  0

a = 3, b = -4, c = 5

Roots are  

x  =  [ - b ± √(b^2 - 4ac) ] / 2a

x  =  [ - (-4) ± √((-4)^2 - 4(3)(5)) ] / 2(3)

x  =  [ 4  ± √(16 - 60) ] / 6

x  =  [ 4  ± √(-44) ] / 6

x  =  [ 4  ± 2i√11 ] / 6

x  =  [ 4  + 2i√11 ] / 6          ;       x  =  [ 4  - 2i√11 ] / 6

x  =  4/6  + (2i√11/6            ;       x  =   4/6  -  (2i√11)/6

x  =  2/3  + i(2/3)√11          ;       x  =   2/3  -  i(2/3)√11

Answer :

The Solutions are x  =  2/3  + i(2/3)√11  and  x  =  2/3  -  i(2/3)√11.