Question 60849
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solve for x by using the quadratic formula: 9x^2-6x+5=0
thanks so much
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        The solution by @jai_kos is incorrect.

        See my correct solution below.



9x^2-6x+5=0


It is the quadratic equation of the form.


ax^2+bx +c =0


Comparing the equations, we get
a = 9, b = -6 and  c = 5


x = {{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


x = {{{(-(-6) +- sqrt( (-6)^2-4*9*5 ))/(2*9) }}}


x = {{{(6 +- sqrt( 36-180 ))/18 }}}

  
x = {{{(6 +- sqrt(-144))/18 }}}


x = {{{(6 +- 12i)/18 }}} = {{{(1 +- 2i)/3}}}.


Thus the given equation has no real solutions.
It has two conjugate solutions in complex numbers.


Solved correctly.