1) 5х²=25х 2) 100х²-16=0 3) 3х²-11х-4=0 4) х²-3х+1=0 5) 2х²+5х+9=х+2 6) (х-4)(4х+6)=(х-5)² 7) 3х²+6х/2=4-2х

Решим уравнения:

1) 5 * х^2 = 25 * х; 

5 * x^2 - 25 * x = 0;

5 * x * (x - 5) = 0;

{ x = 0;

x - 5 = 0;

{ x = 0;

x = 5;

2) 100 * х^2 - 16 = 0; 

(10 * x)^2 - 4^2 = 0; 

(10 * x + 4) * (10 * x - 4) = 0; 

{ 10 * x + 4 = 0; 

10 * x - 4 = 0; 

{ 10 * x = -4; 

10 * x = 4; 

{ x = -4/10; 

x = 4/10; 

{ x = -2/5; 

x = 2/5; 

3) 3 * х^2 - 11 * х - 4 = 0; 

D = 121 + 4 * 3 * 4 = 169; 

x1 = (11 + 13)/6 = 24/6 = 4;

x2 = (11 - 13)/6 = -2/6 = -1/3;

4) х^2 - 3 * х + 1 = 0; 

x₁ = (3 - √5)/(2·1) ≈ 0.38197; 

x₂ = (3 + √5)/(2·1) ≈ 2.6180; 

5) 2 * х^2 + 5 * х + 9 = х + 2; 

2 * x^2 + 4 * x + 7 = 0;

D = b^2 - 4 * a * c = 4^2 - 4 · 2 · 7 = 16 - 56 = -40; 

Уравнение не имеет корней. 

6) (х - 4) * (4 * х + 6) = (х - 5)^2;  

4 * x^2 + 6 * x - 16 * x - 24 = x^2 - 10 * x + 25; 

4 * x^2 - 10 * x - 24 - x^2 + 10 * x - 25 = 0; 

3 * x^2 - 24 - 25 = 0; 

3 * x^2 - 49 = 0; 

x^2 = 49/3; 

x = +-7/√3; 

7) (3  * х^2 + 6 * х)/2 = 4 - 2 * х; 

3 * x^2 + 6 * x = 8 - 4 * x; 

3 * x^2 + 6 * x + 4 * x - 8 = 0; 

3 * x^2 + 10 * x - 8 = 0; 

x = 2/3 и х = -4.