24x^2-280x+600=0

解

24 x^{2} - 280 x + 600 = 0

x = \frac{5 ( 7 + 13 )}{6}, x = \frac{5 ( 7 - 13 )}{6}

十進法表記

x = 8.83795 \dots, x = 2.82870 \dots

解答ステップ

24 x^{2} - 280 x + 600 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 280 ) \pm ( - 280 ) ^{2} - 4 \cdot 24 \cdot 600}{2 \cdot 24}

(- 280)^{2} - 4 \cdot 24 \cdot 600 = 4013

x_{1, 2} = \frac{- ( - 280 ) \pm 40 13}{2 \cdot 24}

解を分離する

x_{1} = \frac{- ( - 280 ) + 40 13}{2 \cdot 24}, x_{2} = \frac{- ( - 280 ) - 40 13}{2 \cdot 24}

x = \frac{- ( - 280 ) + 40 13}{2 \cdot 24} : \frac{5 ( 7 + 13 )}{6}

x = \frac{- ( - 280 ) - 40 13}{2 \cdot 24} : \frac{5 ( 7 - 13 )}{6}

二次equationの解:

x = \frac{5 ( 7 + 13 )}{6}, x = \frac{5 ( 7 - 13 )}{6}