Question 155420
Solve for x:
{{{12/sqrt(5x+6) = sqrt(2x+5)}}} Multiply both sides by{{{sqrt(5x+6)}}}
{{{12 = sqrt(2x+5)*sqrt(5x+6)}}}Simplify the right side.
{{{12 = sqrt((2x+5)*(5x+6))}}} Now square both sides.
{{{144 = (2x+5)(5x+6)}}} Perform the indicated multiplication.
{{{144 = 10x^2+37x+30}}} Subtract 144 from both sides.
{{{10x^2+37x-114 = 0}}} Solve by the quadratic formula:{{{x = (-b+-sqrt(b^2-4ac))/2a}}} where: a = 10, b = 37, and c = -114.
{{{x = (-37+-sqrt((37)^2-4(10)(-114)))/2(10)}}} Simplify.
{{{x = (-37+-sqrt(1369-(-4560)))/20}}}
{{{x = (-37+-sqrt(5929))/20}}}
{{{x = (-37+77)/20}}} or {{{x = (-37-77)/20}}}
{{{x = 2}}} or {{{x = -5.7}}}