(5t-9)^2-7(5t-9)+6=0

解

(5 t - 9)^{2} - 7 (5 t - 9) + 6 = 0

t = 3, t = 2

解答ステップ

(5 t - 9)^{2} - 7 (5 t - 9) + 6 = 0

拡張

(5 t - 9)^{2} - 7 (5 t - 9) + 6 : 25 t^{2} - 125 t + 150

25 t^{2} - 125 t + 150 = 0

解くとthe二次式

t_{1, 2} = \frac{- ( - 125 ) \pm ( - 125 ) ^{2} - 4 \cdot 25 \cdot 150}{2 \cdot 25}

(- 125)^{2} - 4 \cdot 25 \cdot 150 = 25

t_{1, 2} = \frac{- ( - 125 ) \pm 25}{2 \cdot 25}

解を分離する

t_{1} = \frac{- ( - 125 ) + 25}{2 \cdot 25}, t_{2} = \frac{- ( - 125 ) - 25}{2 \cdot 25}

t = \frac{- ( - 125 ) + 25}{2 \cdot 25} : 3

t = \frac{- ( - 125 ) - 25}{2 \cdot 25} : 2

二次equationの解:

t = 3, t = 2