Answer:
0 real solutions
Explanation:
First, we need to transform the equation into the form:
[tex]ax^2+bx+c=0[/tex]So, the initial equation is equivalent to:
[tex]\begin{gathered} 4x^2-8x+10=-x^2-5 \\ 4x^2-8x+10+x^2+5=-x^2-5+x^2+5 \\ 5x^2-8x+15=0 \end{gathered}[/tex]Now, the discriminant can be calculated as:
[tex]b^2-4ac[/tex]If the discriminant is greater than 0, the equation has 2 real solutions.
If the discriminant is equal to 0, the equation has 1 real solution
If the discriminant is less than 0, the equation has 0 real solutions
So, in this case, a is 5, b is -8 and c is 15. Then, the discriminant is equal to:
[tex](-8)^2-4\cdot5\cdot15=84-300=-236[/tex]Since the discriminant is less than zero, the equation has 0 real solutions
