Question 80798
QUESTION:


solve by using the quadratic formula
3x^2=11x+4


ANSWER:

General form of a quadratic equation is,

ax^2 + bx + c = 0 ----------------(1)


Given equation is,

3x^2=11x+4


This can be written in the standered form by transforming  each term on the right side to left side as follows:

3x^2 - 11x - 4 = 0 -----------------(2)


Compare (1) and (2).... we have,


a = 3 , b = -11 and c = -4


Using quadratic formula, the solution of this equation is given by,



{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


Substitute the values of a, b and c in this formula.... we have,




{{{x = ( -(-11) +- sqrt( (-11)^2-4*3*(-4) ))/(2*3)}}} 





{{{x = (11 +- sqrt( 121+48 ))/(6)}}} 




{{{x = (11 +- sqrt( 169))/(6) }}}




{{{x = (11 +- 13)/(6)}}}  





==> x = ( 11 + 13 )/6    or x = (11 - 13 ) /6




==> x = 24/6   or x = -2/6




==> x = 4   or   x = -1/3 , which is the required solution.




Hope you understood.


Regards.


Praseena.