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受欢迎的代数 >

3/2 (4x^2-20x+60)=0

解答

\frac{3}{2} (4 x^{2} - 20 x + 60) = 0

解答

x = \frac{5}{2} + i \frac{35}{2}, x = \frac{5}{2} - i \frac{35}{2}

求解步骤

\frac{3}{2} (4 x^{2} - 20 x + 60) = 0

在两边乘以

2

3 (4 x^{2} - 20 x + 60) = 0

展开

3 (4 x^{2} - 20 x + 60) : 12 x^{2} - 60 x + 180

12 x^{2} - 60 x + 180 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 60 ) \pm ( - 60 ) ^{2} - 4 \cdot 12 \cdot 180}{2 \cdot 12}

化简

(- 60)^{2} - 4 \cdot 12 \cdot 180 : 1235 i

x_{1, 2} = \frac{- ( - 60 ) \pm 12 35 i}{2 \cdot 12}

将解分隔开

x_{1} = \frac{- ( - 60 ) + 12 35 i}{2 \cdot 12}, x_{2} = \frac{- ( - 60 ) - 12 35 i}{2 \cdot 12}

x = \frac{- ( - 60 ) + 12 35 i}{2 \cdot 12} : \frac{5}{2} + i \frac{35}{2}

x = \frac{- ( - 60 ) - 12 35 i}{2 \cdot 12} : \frac{5}{2} - i \frac{35}{2}

二次方程组的解是:

x = \frac{5}{2} + i \frac{35}{2}, x = \frac{5}{2} - i \frac{35}{2}

作图

流行的例子

x^{2} - 5 a + 8 x = 0

solvefor t,g(t-1)=5-(t-1)^2

so l v e f or t, g (t - 1) = 5 - (t - 1)^{2}

solvefor x,f(x-2)=x^2+4x+7

so l v e f or x, f (x - 2) = x^{2} + 4 x + 7

2 x^{2} - 3 x + 1 = 38

solvefor y,x^2+y^2=Ce^{2x}

so l v e f or y, x^{2} + y^{2} = C e^{2 x}