Question

6x²+x-1=0 equacao do 2 grau

Answer 1

6x² + x - 1 = 0
a = 6, b = 1, c = - 1

Δ = b² - 4ac
Δ = 1² - 4 . 6 . (- 1)
Δ = 1 + 24
Δ = 25

x = (- b ± √Δ)/2a
x = (- 1 ± √25)/(2 . 6)
x = (- 1 ± 5)/12

x' = (- 1 + 5)/12 = 4/12 = 1/3
x'' = (- 1 - 5)/12 = - 6/12 = - 1/2

x = 1/3
x = - 1/2

Answer 2

Equação do 2° grau

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

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