Question 80825
Solve for x:
{{{x^2 = 5x+8}}} 
First, get your equation into the standard form for quadratic equations: {{{ax^2+bx+c = 0}}} by subtracting 5x from both sides then subtracting 8 from both sides.
{{{x^2-5x-8 = 0}}} Compare this with the standard form and you can see that, in your equation, a = 1, b = -5, and c = -8.  Now apply the quadratic formula:{{{x = (-b+-sqrt(b^2-4ac))/2a}}} to your equation.
{{{x = (-(-5)+-sqrt((-5)^2-4(1)(-8)))/2(1)}}} Simplify this.
{{{x = (5+-sqrt(25+32))/2}}}
{{{x = (5+-sqrt(57))/2}}}
The solutions are:
{{{x = (5+sqrt(57))/2}}} or {{{x = (5-sqrt(57))/2}}}