In order to solve this quadratic formula, we will use the quadratic formula, which is #(-b+-sqrt(b^2-4ac))/(2a)#.
In order to use it, we need to understand which letter means what. A typical quadratic function would look like this: #ax^2 + bx + c#. Using that as a guide, we will assign each letter with their corresponding number and we get #a=8#, #b=-16#, and #c=-15#.
Then it is a matter of plugging in our numbers into the quadratic formula. We will get: #(-(-16)+-sqrt((-16)^2-4(8)(-15)))/(2(8))#.
Next, we will cancel out signs and multiply, which we will then get:
#(16+-sqrt(256+480))/16#.
Then we will add the numbers in the square root and we get #(16+-sqrt(736))/16#.
Looking at #sqrt(736)# we can probably figure out that we can simplify it. Let's use #16#. Dividing #736# by #16#, we will get #46#. So the inside becomes #sqrt(16*46)#. #16# is a perfect square root and the square of it is #4#. So carrying out #4#, we get #4sqrt(46)#.
Then our previous answer, #(16+-sqrt(736))/16#, becomes #(16+-4sqrt(46))/16#.
Notice that #4# is a factor of #16#. So taking our #4# from the numerator and denominator: #(4/4)(4+-sqrt(46))/4#. The two fours cancel out and our final answer is:
#(4+-sqrt(46))/4#.
