Problem: what is 4x^2=7x-3
4x^2 = 7x - 3
4x^2 - 7x + 3 = 0
-b ± sqrt(b² - 4*a*c)
x = -----------------------------
2a
-(-7) ± sqrt(-7² - 4*4*3)
x = -----------------------------
2(4)
7 ± sqrt(49 - 48)
x = --------------------
8
7 ± sqrt(1)
x = --------------
8
7 ± 1
x = ---------
8
7 + 1 7 - 1
x = --------- and x = ---------
8 8
8 6
x = ----- and x = ----
8 8
x = 1 and x = 3/4
Check.
4x^2 = 7x - 3
4(1)^2 = 7(1) - 3
4 * 1 = 7 - 3
4 = 4
4x^2 = 7x - 3
4(3/4)^2 = 7(3/4) - 3
4(9/16) = 21/4 - 3
9/4 = 21/4 - 12/4
9/4 = 9/4
Answer: x = 1 and x = 3/4