Question 3229
I assmue you mean {{{x^2 - 5x + 3 = 0}}}<br>

To find a solution we will need to apply the quadratic equation, which says the roots of a quadratic equation in the form {{{ax^2 + bx + c = 0}}}are:<br>
{{{(-b +- sqrt(b^2 - 4ac))/(2a)}}}<br>.
To use the quadratic equation we must first a, b and c, which, for this problem, are a = 1, b = -5 and c = 3. Substituting them into the quadratic, we get:<br>
{{{(5 +- sqrt((-5)^2 - 4(1)(3)))/2(1) = (5 +- sqrt(25 - 12))/2 = (5 +- sqrt(13))/2}}}<br>.
So there are two roots to this eqaution, {{{x = (5 + sqrt(13))/2}}} and {{{x = (5 - sqrt(13))/2}}}. To test the correctness of this answer, substitute the roots in to the equation.<br>
{{{((5 + sqrt(13))/2)^2 - 5((5 + sqrt(13))/2) + 3 = 0}}} and <br>
{{{((5 - sqrt(13))/2)^2 - 5((5 - sqrt(13))/2) + 3 = 0}}}<br>
Get a calculator and check them out. Thes equations hold, therefore 
 {{{x = (5 + sqrt(13))/2}}} and {{{x = (5 - sqrt(13))/2}}} are solutions to the equation.