407k^2+480k-69=0

解

407 k^{2} + 480 k - 69 = 0

k = \frac{- 240 + 169 3}{407}, k = - \frac{240 + 169 3}{407}

十進法表記

k = 0.12952 \dots, k = - 1.30888 \dots

解答ステップ

407 k^{2} + 480 k - 69 = 0

解くとthe二次式

k_{1, 2} = \frac{- 480 \pm 48 0 ^{2} - 4 \cdot 407 ( - 69 )}{2 \cdot 407}

48 0^{2} - 4 \cdot 407 (- 69) = 3383

k_{1, 2} = \frac{- 480 \pm 338 3}{2 \cdot 407}

解を分離する

k_{1} = \frac{- 480 + 338 3}{2 \cdot 407}, k_{2} = \frac{- 480 - 338 3}{2 \cdot 407}

k = \frac{- 480 + 338 3}{2 \cdot 407} : \frac{- 240 + 169 3}{407}

k = \frac{- 480 - 338 3}{2 \cdot 407} : - \frac{240 + 169 3}{407}

二次equationの解:

k = \frac{- 240 + 169 3}{407}, k = - \frac{240 + 169 3}{407}