13x-14x²-3=0 -25х²+16=0 -х²-18-19х=0 х²+4х=0 -4-3х²+7х=0дискриминант

Чтобы решить уравнения, сначала перепишем их в стандартном виде:

1) 13х - 14х^2 - 3 = 0;

-14х^2 + 13х - 3 = 0.

D = b^2 - 4ac = 169 - 4 * 14 * 3 = 169 - 168 = 1.

x1 = (-b + √D)/2a = (-13 + 1)/(-28) = 12/28 = 3/7;

x2 = (-b - √D)/2a = (-13 - 1)/(-28) = 14/28 = 1/2.

2) -25x^2 + 16 = 0.

-25x^2 = - 16;

x^2 = 16/25;

x = ± 4/5.

(D = 0 + 4 * 25 * 16 = 1600).

3) -x^2 - 18 - 19x = 0.

-x^2 - 19x - 18 = 0.

D = 361 - 4 * 1 * 18 = 361 - 72 = 289.

x1 = (19 + 17)/(-2) = 36/(-2) = -18.

x2 = (19 - 17)/(-2) = -1.

4) x^2 + 4x = 0.

D = 16 - 4 * 1 * 0 = 16.

x1 = (-4 + 4)/2 = 0;

x2 = (-4 - 4)/2 = -4.

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

-3x^2 + 7x - 4 = 0.

D = 49 - 4 * 3 * 4 = 49 - 48 = 1.

x1 = (-7 + 1)/(-6)= 1.

x2 = (-7 - 1)/(-6) = 1 1/3.