Use the discriminant to decide how many solutions the given equation will have. Show all work for credit. 6x^2-2x=3

two real, unequal roots.

Step-by-step explanation:

I will assume that you meant 6x^2 - 2x = 3, which is equivalent to

6x^2 - 2x - 3 = 0. The coefficients are a = 6, b = - 2 and c = - 3.

The discriminant is b^2 - 4ac, which here is

(-2) ^2 - 4 (6) (-3) = 4 + 72 = 76

Because the discriminant is + we can conclude that the given equation has two real, unequal roots.