Solve for x
3xsquared - 4x-2=0
Use the quadratic formula to solve for x.
3x^2 - 4x - 2 = 0
From the general equation, ax^2 + bx + c = 0,
we get: a = 3, b = -4 and c = -2
-b ± √(b^2 - 4(ac)
x = ---------------------------
2a
-(-4) ± √((-4)^2 - 4(3(-2))
x = --------------------------------
2(3)
4 ± √(16 - (-24))
x = ----------------------
6
4 ± √(16 + 24)
x = ------------------
6
4 ± √(40)
x = ------------
6
4 ± 6.324555
x = -----------------
6
10.324555 -2.324555
x = -------------- x = --------------
6 6
x = 1.72076 x = -0.387426
Substitute those values into the original equation
to verify your answers.
3x^2 - 4x - 2 = 0
3(1.72076^2) - 4(1.72076) - 2 = 0
3(2.961015) - 6.88304 - 2 = 0
8.88304 - 6.88304 - 2 = 0
2 - 2 = 0
0 = 0
3x^2 - 4x - 2 = 0
3(-0.387426^2) - 4(-0.387426) - 2 = 0
3(.150099) + 1.549704 - 2 = 0
0.450296 + 1.549704 - 2 = 0
2 - 2 = 0
0 = 0