Question

How many solutions does the equation `6x^2 -2x = -9` have?

Answer 1

No real solutions

Explanation:

If we look at the formula for solving a quadratic
`x =(-b+-sqrt(b^2-4ac))/(2a)` we can see the determinant. `b^2-4ac`

This is the bit that determines whether the equation has 2 real roots, 1 root or no real roots
If the determinant is greater than zero there are 2 real roots, if it is zero there is one solution ( the graph of the equation touches the x axis)
In this case `b^2-4ac`=`(-2)^2-4*6*9`=-212
There is no real number which is `sqrt(-216)`

The graph of this equation does not cross the x axis