solvefor x,3x^2-5x-1=0

解

x, 3 x^{2} - 5 x - 1 = 0

x = \frac{5 + 37}{6}, x = \frac{5 - 37}{6}

十進法表記

x = 1.84712 \dots, x = - 0.18046 \dots

解答ステップ

3 x^{2} - 5 x - 1 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 3 ( - 1 )}{2 \cdot 3}

(- 5)^{2} - 4 \cdot 3 (- 1) = 37

x_{1, 2} = \frac{- ( - 5 ) \pm 37}{2 \cdot 3}

解を分離する

x_{1} = \frac{- ( - 5 ) + 37}{2 \cdot 3}, x_{2} = \frac{- ( - 5 ) - 37}{2 \cdot 3}

x = \frac{- ( - 5 ) + 37}{2 \cdot 3} : \frac{5 + 37}{6}

x = \frac{- ( - 5 ) - 37}{2 \cdot 3} : \frac{5 - 37}{6}

二次equationの解:

x = \frac{5 + 37}{6}, x = \frac{5 - 37}{6}