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受欢迎的代数 >

(3/2 x+5)*(7/2 x-6)=30

解答

(\frac{3}{2} x + 5) \cdot (\frac{7}{2} x - 6) = 30

解答

x = \frac{8}{3}, x = - \frac{30}{7}

+1

十进制

x = 2.66666 \dots, x = - 4.28571 \dots

求解步骤

(\frac{3}{2} x + 5) (\frac{7}{2} x - 6) = 30

展开

(\frac{3}{2} x + 5) (\frac{7}{2} x - 6) : \frac{21}{4} x^{2} + \frac{17}{2} x - 30

\frac{21}{4} x^{2} + \frac{17}{2} x - 30 = 30

将

30

para o lado esquerdo

\frac{21}{4} x^{2} + \frac{17}{2} x - 60 = 0

改写成标准形式

a x^{2} + b x + c = 0

\frac{21 x ^{2}}{4} + \frac{17 x}{2} - 60 = 0

使用求根公式求解

x_{1, 2} = \frac{- \frac{17}{2} \pm ( \frac{17}{2} ) ^{2} - 4 \cdot \frac{21}{4} ( - 60 )}{2 \cdot \frac{21}{4}}

(\frac{17}{2})^{2} - 4 \cdot \frac{21}{4} (- 60) = \frac{73}{2}

x_{1, 2} = \frac{- \frac{17}{2} \pm \frac{73}{2}}{2 \cdot \frac{21}{4}}

将解分隔开

x_{1} = \frac{- \frac{17}{2} + \frac{73}{2}}{2 \cdot \frac{21}{4}}, x_{2} = \frac{- \frac{17}{2} - \frac{73}{2}}{2 \cdot \frac{21}{4}}

x = \frac{- \frac{17}{2} + \frac{73}{2}}{2 \frac{21}{4}} : \frac{8}{3}

x = \frac{- \frac{17}{2} - \frac{73}{2}}{2 \frac{21}{4}} : - \frac{30}{7}

二次方程组的解是:

x = \frac{8}{3}, x = - \frac{30}{7}

作图

流行的例子

1/4 (4u+12)-1=12

\frac{1}{4} (4 u + 12) - 1 = 12

∣ 6 - 3 x ∣ - 6 = 9

\frac{x - 1}{x + 2} > 0

x^{2} + 4 x \leq 0

2 x^{2} + 9 x = 0