Question

for what value of m does the quadratic equation mx(5x-6)+9=0 has two equal roots

Answer 1

$mx(5x - 6) + 9 = 0$
$5m {x}^{2} - 6mx + 9 = 0 \\ for \: equal \: roots \: {b}^{2} - 4ac = 0 \\ {(- 6m)}^{2} - 4(5m)9 = 0 \\ 36 {m}^{2} - 180m = 0 \\ 36m(m - 5) = 0 \\ m = 0 \: or \: \: m - 5 = 0 \\ m = 0 \: \: or \: \: m = 5$

Answer 2

mx(5x-6)+9=0 5mx²-6mx+9=0 For an eq. to have equal roots,  D=b²-4ac=0 (-6m) ²-4(5m)(9)=0 =>36m²-180m=0 =>m=5