The roots of this quadratic equation need to be found using the quadratic formula or the completing the squares method.
Factoring will not do it because the roots are not integers.
The quadratic formula is
Your formula starts out as
Subtract 4x from both sides of this equation to get .
Now the equation is in the standard form of a quadratic equation.
The standard form is
In your equation:
a = 3
b = -4
c = -2
In the quadratic formula, this makes:
-b = 4
2a = 6 = which simplifies to = 6.32455532
Placing these values into the quadratic formula gets you:
x = 1.72075922 and x = -.387425887
Those are your roots.
You confirm by replacing x in your original equation with these values to determine if the equations are true or not.
For example:
When you replace x with -.387425887, your original equation becomes:
3*(-.387425887)^2 - 4*(-.387425887) - 2 = 0 which simplifies to:
.450296453 - (1.549703547) - 2 = 0 which simplifies to:
2 - 2 = 0 which is true, confirming that the value of x = -.387425887 is good.
