Question 707165
{{{3q(q-2)=6}}}
First simplify so we can see what kind of equation we have. Using the Distributive Property to multiply we get:
{{{3q^2-6q=6}}}
This is a quadratic equation (because of the squared term). To solve it we first want one side to be zero. Subtracting 6 from each side:
{{{3q^2-6q-6=0}}}
Now we factor (or use the Quadratic Formula). We can factor out the greatest common factor of 3:
{{{3(q^2-2q-2)=0}}}
But now it won't factor anymore. So we must resort to the Quadratic Formula. We can use the formula on {{{3q^2-6q-6}}} or on {{{q^2-2q-2}}}. (The answers will be the same either way.) I'm going to use the formula on {{{q^2-2q-2}}} because the a, b and c values are smaller.
{{{q = (-(-2) +- sqrt((-2)^2-4(1)(-2)))/2(1)}}}
Simplifying...
{{{q = (-(-2) +- sqrt(4-4(1)(-2)))/2(1)}}}
{{{q = (-(-2) +- sqrt(4+8))/2(1)}}}
{{{q = (-(-2) +- sqrt(12))/2(1)}}}
{{{q = (2 +- sqrt(12))/2}}}
{{{q = (2 +- sqrt(4*3))/2}}}
{{{q = (2 +- sqrt(4)*sqrt(3))/2}}}
{{{q = (2 +- 2*sqrt(3))/2}}}
{{{q = (2(1 +- sqrt(3)))/2}}}
{{{q = 1 +- sqrt(3)}}}
which is short for:
{{{q = 1 + sqrt(3)}}} or {{{x = 1 - sqrt(3)}}}
These are the two solutions to your equation.