How do you solve 3x2 minus 18x equals 0 also solve x2 minus 10x plus 24 equals zero also solve 2x2 minus 3x equals 8?

Answer 1

You really should ask these questions separately, but....

3x2 - 18x = 0

∴ (3x)(x - 6) = 0

∴ x ∈ {0, 6}

x2 - 10x + 24 = 0

∴ (x - 6)(x - 4) = 0

∴ x ∈ {4, 6}

2x2 - 3x = 8

∴ 4x2 - 6x = 16

∴ 4x2 - 6x + (3/2)2 = 16 + (3/2)2

∴ (2x - 3/2)2 = 16 + 9/4

∴ 2x - 3/2 = (73/4)1/2

∴ 2x = 3/2 ± √(73/4)

∴ 2x = (3 ± √73) / 2

∴ x = (3 ± √73) / 4

∴ x ∈ {(3 - √73) / 4 , (3 + √73) / 4}