Solve by using the quadratic formula.
3x^2=11x+4.
Look up the formula if you don't know it already.
In this case a = 3, b = -11 and c = -4.
You get that by rewriting the equation in the standard form ax^2 + bx + c = 0 , where a, b, and c are constants.
To solve the equation 3x^2 = 11x + 4 using the quadratic formula, we need to plug the values of a, b, and c into the formula and perform the necessary calculations.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -11, and c = -4. Substituting these values into the quadratic formula gives:
x = (-(-11) ± √((-11)^2 - 4(3)(-4))) / (2(3))
Now, we simplify the expression further:
x = (11 ± √(121 + 48)) / 6
x = (11 ± √169) / 6
Since √169 = 13, we can simplify the expression:
x = (11 ± 13) / 6
Now, we can find the two possible values for x by evaluating the expression with both the positive and negative square root:
x1 = (11 + 13) / 6 = 24 / 6 = 4
x2 = (11 - 13) / 6 = -2 / 6 = -1/3
Hence, the two solutions to the quadratic equation 3x^2 = 11x + 4 are x = 4 and x = -1/3.