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

1 Answer
Aug 26, 2016

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