Find the root of the following quadratic equations, if they exist, by using the quadratic formula by Shridharacharya Method:

Let us solve the above equation by equating it to zero,

-2 = 3(x² – 2x)

3x² – 6x + 2 = 0

When we compare the above quadratic equation with the generalized one we get,

ax² + bx + c = 0

a = 3

b = -6

c = 2

There is one formula developed by Shridharacharya to determine the roots of a quadratic equation which is as follows:

Before putting the values in the formula let us check the nature of roots by b² – 4ac >0

⟹ (-6)² – (4 × 3 × 2)

⟹ 36 – 24

⟹ 12

Since b² – 4ac = 5 the roots are real and distinct.

Now let us put the values in the above formula