Question 1143059
expression is 12b^2 - 29b + 15


set the expression equal to 0 to get the equation of 12b^2 - 29b + 15 = 0


replace b with x to get the equation of 12x^2 - 29x + 15 = 0.



use the quadratic formula to solve for x in this quadratic equation that is now in standard form of ax^2 + bx + c = 0.


a = 12
b = -29
c = 15


quadratic formula is x = (-b + sqrt(b^2-4ac)/(2a) or x = (-b - sqrt(b^2-4ac)/(2a)


first formula becomes x = (29 + 11) / 24 = 5/3.


second formula becomes x = (29 - 11) / 24 = 3/4.


those are the roots of the given equation.


replace x with b and you get b = 5/3 or b = 3/4.