15y^2 + 19y + 6 = 0
a = 15, b = 19, c = 6 use the quadratic formula
{-b +- sqrt(b^2 - 4ac)}/2a plug in
{-19 +- sqrt(19^2 - 4*15*6)}/2*15
{-19 +- sqrt(361 - 360)} /30
(-19 + - 1)/30
(-19+1)/30 or (-19 - 1)/30
-18/30 or -20/30
-6/10 or -2/3
-3/5
CHECK:
15y^2+19y+6=0
15*(-3/5^2) + 19*(-3/5) + 6 = 0
15 (9/25) + -57/5 + 6 = 0
27/5 - 57/5 + 30/5 = 0
0 = 0 checks
15y^2+19y+6=0
15 * (-2/3^2) + 19 * (-2/3) + 6 = 0
15*(4/9) - 18/3 + 6 = 0
20/3 - 18/3 + 18/3 = 0
20/3 = 0 not a solution