Question

resolva as equações 

6x² + x - 1 = 0

Answer 1

6x² + x - 1 = 0

a= 6; b=1; c=-1

 

Delta= b² -4.a.c
Delta= (1)² - 4.6.(-1)
Delta = 1 + 24
Delta = 25

x = -b ±√Delta / 2.a
x  = -(1) ±√25 / 2.6
x = -1 ± 5 / 12

x ¹= -1+5 / 12
x ¹  = 4/12 simplifica por 2

x¹ =2/6 simplifica por 2

x¹ = 1/3

x² = -1-5 / 12
x² = -6/12 simplifica por 2
x² = -3/6 simplifica por 3

x²= -1/2

Answer 2

Equação do 2° grau

$6 {x}^{2} +x - 1 = 0 \\ \\ a = 6 \\ b = 1 \\ c = ( - 1) \\ \\ \Delta = {b}^{2} - 4ac \\ \Delta = {1}^{2} - 4 \cdot6 \cdot( - 1) \\\Delta = 1 - 24 \cdot( - 1) \\ \Delta = 1 + 24 \\ \Delta = 25 \\ \\ x = \frac{ - b\pm \sqrt{\Delta} }{2a} \\ \\ x = \frac{ - 1\pm \sqrt{25} }{2 \cdot6 } \\ \\ x = \frac{ - 1\pm 5 }{12} \\ \\ x_{1} = \frac{ - 1 + 5}{12} = \frac{ {4}^{\color{red} { \div 4}} }{ {12}^{\color{red} { \div 4}} } = \bf{ \frac{1}{3} } \\ \\ x_{2} = \frac{ - 1 - 5}{12} = - \frac{ {6}^{\color{red} { \div 6}} }{ {12}^{\color{red} { \div 6}} } = - \bf{ \frac{1}{2} }$

$\boxed{ \bf{S = \{ - \frac{1}{2} , \: \frac{1}{3} \} } }$