Решите уравнение, используя формулу:
а) 3х² - 14х + 16 = 0; б) 5х² - 16х + 3= 0;
в) х² + 2х - 80 = 0;     г) х² - 22x - 23 = 0;
д) 4х² - 36x + 77 = 0; е) 15у² - 22у -37 = 0;
ж) 7z² - 20z + 14 = 0; з) у² - 10y - 25 = 0.

Решение:


а) 3х² - 14х + 16 = 0; D = 14₂ - 4 • 3 • 16 = 196 - 192 = 4; x = (14±2)/6; x₁ = 2; x₂ = 16/6 = 2 2/3;
б) 5х² - 16х + 3= 0; D = 16² - 4 • 5 • 3 = 256 - 60 = 196; x = (16±14)/10; x₁ = 0,2; x₂ = 3;
в) х² + 2х - 80 = 0; D = 4 + 4 • 80 = 4 + 320 = 324; x = (-2±18)/2 = -1 ± 9; x₁ = -10; x₂ = 8;
г) х² - 22x - 23 = 0; D = 22² + 4 • 23 = 4844 - 92 = 576; x = (22±24)/2; x₁ = -1; x₂ = 23;
д) 4х² - 36x + 77 = 0; D = 36² - 4 • 4 • 77 = 1296 - 1232 = 64; x = (36±8)/8; x₁ = 3,5; x₂ = 5,5;
е) 15у² - 22у -37 = 0; D = 22² + 4 • 15 • 37 = 484 + 2220 = 2704; x = (22±52)/30; x₁ = -1; x₂ = 74/30 = 2 7/15;
ж) 7z² - 20z + 14 = 0; D = 20² - 4 • 7 • 14 = 400 - 392 = 8; z = (20±√8)/2•7 = (10±√2)/7;
з) у² - 10y - 25 = 0; D = 10² + 4 • 25 = 200; D = (10±√200)/2 = 5 ± 5√2.