Determine the type and number of solution the following equa

Determine the type and number of solution the following equation have 2x^2-1/3x+1/5=0 1/6x^2+4x+7=0

a) 2x^2 -x/3 1x/5 =0

Mulitply the equation 15

30x^2 -5x +3 =0

Solve by using quadratice formula:

x = (-b +/- sqrt(b^2 -4ac)/2a

= ( 5+ /- sqrt( 25 -4*3*30)/60

= (5+/- isqrt335)/60

So, there are two solutions and both are complx roots

b) x^2/6 + 4x +7 =0

Multiply by 6 we get

x^2 +24x +42 =0

Using quadratic root formula:

x =(-b +/- sqrt(b^2 -4ac)/2a

= ( -24 + /- sqrt( 24^2 -4*42)/2

=( -24 + /- sqrt408)/2

So, there are two solutions and both are real roots