Question 65840
Rearrange the equation to get it in the {{{ax^2+bx+c=0}}} form.
{{{5x=x^2-3}}}
Subtract 5x from each side.
{{{5x-5x=x^2-5x-3}}}
{{{x^2-5x-3=0}}}
The discriminant is found using the formula 
{{{b^2-4*a*c}}}
In this example a=1, b=-5 and c=-3
{{{(-5)^2-4*1*(-3)}}}
{{{25-(-12)}}}
=37
The number is positive so there will be two real solutions to the equation.
(a value of zero implies one solution and a negative value implies no real solution but two solutions involving complex numbers.)