Question 245847
{{{(4x+1)^2 = 3x+4}}}
To use the quadratic formula, {{{x = (-b +- sqrt(b^2 - 4ac))/2a}}}, your equation needs to be in {{{ax^2 + bx + c = 0}}} form. So getting the equation into the proper form is where we start.
Multiply out the left side:
{{{16x^2 + 8x + 1 = 3x + 4}}}
Make the right side zero by subtracting 3x and 4 from each side:
{{{16x^2 + 5x - 3 = 0}}}
Now we have the proper form and we can use the quadratic formula with "a" = 16, "b" = 5 and "c" = -3:
{{{x = (-(5) +- sqrt((5)^2 - 4(16)(-3)))/2(16)}}}
Now we simplify:
{{{x = (-(5) +- sqrt(25 - 4(16)(-3)))/2(16)}}}
{{{x = (-5 +- sqrt(25 + 192))/32}}}
{{{x = (-5 +- sqrt(217))/32}}}
So
{{{x = (-5 + sqrt(217))/32}}} or {{{x = (-5 - sqrt(217))/32}}}