Question 420637
{{{-3x^2 + 75x=125+6x}}}
Because of the squared term this is a quadratic equation. To solve a quadratic equation we want one side to be zero. And since the rest of the problem will be easier if the squared term has a positive coefficient, I am going to subtract the entire left side from both sides of the equation:
{{{0 = 3x^2 - 69x + 125}}}
This equation does not factor so we will use the Quadratic Formula:
{{{x = (-(-69) +- sqrt((-69)^2 - 4(3)(125)))/2(3)}}}
which simplifies as follows:
{{{x = (-(-69) +- sqrt(4761 - 4(3)(125)))/2(3)}}}
{{{x = (-(-69) +- sqrt(4761 - 1500))/2(3)}}}
{{{x = (-(-69) +- sqrt(3261))/2(3)}}}
{{{x = (69 +- sqrt(3261))/6}}}
There are no perfect square factors in 3261 so the square root will not simplify. The solutions to your equation are:
{{{x = (69 + sqrt(3261))/6}}} or {{{x = (69 - sqrt(3261))/6}}}