Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve ( notice , , and )
Plug in a=4, b=23, and c=6
Negate 23 to get 23
Square 23 to get 529 (note: remember when you square 23, you must square the negative as well. This is because .)
Multiply to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
Multiply 2 and 4 to get 8
So now the expression breaks down into two parts
or
Lets look at the first part:
Add the terms in the numerator
Divide
So one answer is
Now lets look at the second part:
Subtract the terms in the numerator
Divide
So another answer is
So our solutions are:
or
