3x^2+2sqrt(5)x-5=0

解

3 x^{2} + 25 x - 5 = 0

x = \frac{5}{3}, x = - 5

十進法表記

x = 0.74535 \dots, x = - 2.23606 \dots

解答ステップ

3 x^{2} + 25 x - 5 = 0

解くとthe二次式

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

(25)^{2} - 4 \cdot 3 (- 5) = 45

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

解を分離する

x_{1} = \frac{- 2 5 + 4 5}{2 \cdot 3}, x_{2} = \frac{- 2 5 - 4 5}{2 \cdot 3}

x = \frac{- 2 5 + 4 5}{2 \cdot 3} : \frac{5}{3}

x = \frac{- 2 5 - 4 5}{2 \cdot 3} : - 5

二次equationの解:

x = \frac{5}{3}, x = - 5