Question 401068
When solving quadratic equations you want one side to be zero. So we start by subtracting 6 from each side:
{{{x^2-4x-6=0}}}
This equation will not factor so we must use the Quadratic Formula (or complete the square):
{{{x = (-(-4) +- sqrt((-4)^2-4(1)(-6)))/2(1)}}}
which simplifies as follows:
{{{x = (-(-4) +- sqrt(16-4(1)(-6)))/2(1)}}}
{{{x = (-(-4) +- sqrt(16+24))/2(1)}}}
{{{x = (-(-4) +- sqrt(40))/2(1)}}}
{{{x = (4 +- sqrt(40))/2}}}
{{{x = (4 +- sqrt(4)*sqrt(10))/2}}}
{{{x = (4 +- 2*sqrt(10))/2}}}
{{{x = (2(2 +- sqrt(10)))/2}}}
{{{x = (cross(2)(2 +- sqrt(10)))/cross(2)}}}
{{{x = 2 +- sqrt(10)}}}
In long form this is:
{{{x = 2 + sqrt(10)}}} or {{{x = 2 - sqrt(10)}}}