Answer:
x = -3/2, x = 4
Step-by-step explanation:
4x² - 7x = 3x + 24, first put everything on one side
4x² - 10x - 24 = 0, factor 2 out
2(2x² - 5x - 12) = 0 then factor. You need two numbers that multiply to be -24 and add to be -5, so -8 and 3 are the factors.
(2x² - 8x) + (3x - 12) group them either way and then factor out GCF
2x(x - 4) + 3(x - 4) = 0
(2x + 3)(x - 4) = 0, set each factor = 0 and solve
2x + 3 = 0, 2x = -3, x = -3/2
x - 4 = 0, x = 4
≈5.61