Solve 6x² - 13x + 6 = 0 for x.

First method

6x² - 13x + 6 = 0

(2x - 3)(3x - 2) = 0

x = 3 / 2; 2 / 3

 

Second method

6x² - 13x + 6 = 0

144x² - 312x + 144 = 0

144x² - 312x + 169 = 25

(12x - 13)² = 25

12x - 13 = ±5

12x = 13 ± 5

x = (13 ± 5) / 12

x = 3 / 2; 2 / 3

 

Third method

6x² - 13x + 6 = 0

a = 6, b = -13 and c = 6

b² - 4ac = 25

x = (13 ± √25) / 12

x = (13 ± 5) / 12

x = 3 / 2; 2 / 3

 

Solve 10x² - 29x + 10 = 0 for x.

First method

10x² - 29x + 10 = 0

(2x - 5)(5x - 2) = 0

x = 5 / 2; 2 / 5

 

Second method

10x² - 29x + 10 = 0

400x² - 1,160x + 400 = 0

400x² - 1,160x + 841 = 441

(20x - 29)² = 441

20x - 29 = ±21

20x = 29 ± 21

x = (29 ± 21) / 20

x = 5 / 2; 2 / 5

 

Third method

10x² - 29x + 10 = 0

a = 10, b = -29 and c = 10

b² - 4ac = 441

x = (29 ± √441) / 20

x = (29 ± 21) / 20

x = 5 / 2; 2 / 5

 

Solve 15x² - 34x + 15 = 0 for x.

First method

15x² - 34x + 15 = 0

(3x - 5)(5x - 3) = 0

x = 5 / 3; 3 / 5

 

Second method

15x² - 34x + 15 = 0

225x² - 510x + 225 = 0

225x² - 510x + 289 = 64

(15x - 17)² = 64

15x - 17 = ±8

15x = 17 ± 8

x = (17 ± 8) / 15

x = 5 / 3; 3 / 5

 

Third method

15x² - 34x + 15 = 0

a = 15, b = -34 and c = 15

b² - 4ac = 256

x = (34 ± √256) / 30

x = (34 ± 16) / 30

x = (17 ± 8) / 15

x = 5 / 3; 3 / 5