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

解

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

x = \frac{5 k + 25 k ^{2} + 24}{6}, x = \frac{5 k - 25 k ^{2} + 24}{6}

解答ステップ

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

解くとthe二次式

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

簡素化

(- 5 k)^{2} - 4 \cdot 3 (- 2) : 25 k^{2} + 24

x_{1, 2} = \frac{- ( - 5 k ) \pm 25 k ^{2} + 24}{2 \cdot 3}

解を分離する

x_{1} = \frac{- ( - 5 k ) + 25 k ^{2} + 24}{2 \cdot 3}, x_{2} = \frac{- ( - 5 k ) - 25 k ^{2} + 24}{2 \cdot 3}

x = \frac{- ( - 5 k ) + 25 k ^{2} + 24}{2 \cdot 3} : \frac{5 k + 25 k ^{2} + 24}{6}

x = \frac{- ( - 5 k ) - 25 k ^{2} + 24}{2 \cdot 3} : \frac{5 k - 25 k ^{2} + 24}{6}

二次equationの解:

x = \frac{5 k + 25 k ^{2} + 24}{6}, x = \frac{5 k - 25 k ^{2} + 24}{6}