1) 15x^2+4=16x

15x^2 - 16x + 4 = 0

D = b^2 - 4ac = (-16)^2 - 4154 = 256 - 240 = 16

x1 = (16 + √16)/30 = 20/30 = 2/3
x2 = (16 - √16)/30 = 10/30 = 1/3

2) 7x^2 = 4x - 3

7x^2 - 4x + 3 = 0

D = (-4)^2 - 473 = 16 - 84 = -68

x1 = (4 + √-68)/14 = (4 + 2i√17)/14 = (2 + i√17)/7
x2 = (4 - √-68)/14 = (4 - 2i√17)/14 = (2 - i√17)/7

3) 2x - 5x^2 = 0

-5x^2 + 2x = 0
x(-5x + 2) = 0
x = 0 or -5x + 2 = 0 => x = 2/5

4) 5x^2 - 20 = 0

5x^2 = 20
x^2 = 4
x1 =√4 = 2
x2 = -√4 = -2

5) 7x+3+4x^2=0

4x^2 + 7x + 3 = 0

D = 7^2 - 443 = 49 - 48 = 1

x1 = (-7 + 1)/8 = -3/4
x2 = (-7 - 1)/8 = -1

6) x^2 - 9x + 18 = 0

x^2 - 6x - 3x + 18 = 0
x(x-6) - 3(x - 6) = 0
(x-6)(x-3) = 0

x1 = 6
x2 = 3