We want to use the discriminant of the given quadratic equation to determine the number of real solutions. In the Quadratic Formula, b^2-4ac is the discriminant.
ax^2+bx+c=0 ⇔ x=- b±sqrt(b^2-4ac)/2aIf we just want to know the number of real solutions, and not the solutions themselves, we only need to work with the discriminant. To do so, we will rearrange the equation and identify the values of a, b, and c.
3x^2-x=8 ⇔ 3x^2+( -1)x+( -8)=0
We see that a = 3, b = - 1, and that c = - 8. Finally, let's evaluate the discriminant.
Since the discriminant is 97, the quadratic equation has two real solutions.
Extra
Further information
If the discriminant is greater than zero, the equation will have two real solutions. If it is equal to zero, the equation will have one real solution. Finally, if the discriminant is less than zero, the equation will have no real solutions.
