Answer:
No real roots
Step-by-step explanation:
In order to find the value of the discriminant, we proceed to re-write the quadratic expression with all the terms on one side of the equal sign. First solving the indicated parenthesis preceded by the negative sign, and then by adding [tex]8w^2[/tex] on both sides:
[tex]-8w^{2} = -11w+7\\0=8w^{2} -11w+7[/tex]
now we identify the values [tex]a, b, c[/tex] that appear in the expression of the discriminant: [tex]b^2 -4ac[/tex]
These are:
[tex]a=8\\b=-11\\c=7[/tex]
Therefore:
[tex]b^2 -4ac=(-11)^2 -4*8*7=121-224=-103[/tex]
This is a negative number, which means that the solutions to the quadratic equations are imaginary numbers, and not real numbers.
