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Popular >

6x-8x^2-((x-2))/5 = 1/2 x+3/2-((x-1))/4

Solution

6 x - 8 x^{2} - \frac{( x - 2 )}{5} = \frac{1}{2} x + \frac{3}{2} - \frac{( x - 1 )}{4}

Solution

x = \frac{111}{320} - i \frac{3 551}{320}, x = \frac{111}{320} + i \frac{3 551}{320}

Solution steps

6 x - 8 x^{2} - \frac{( x - 2 )}{5} = \frac{1}{2} x + \frac{3}{2} - \frac{( x - 1 )}{4}

Find Least Common Multiplier of

5, 2, 4 : 20

Multiply by LCM=

20

6 x \cdot 20 - 8 x^{2} \cdot 20 - \frac{x - 2}{5} \cdot 20 = \frac{1}{2} x \cdot 20 + \frac{3}{2} \cdot 20 - \frac{x - 1}{4} \cdot 20

Simplify

120 x - 160 x^{2} - 4 (x - 2) = 10 x + 30 - 5 (x - 1)

Expand

120 x - 160 x^{2} - 4 (x - 2) : - 160 x^{2} + 116 x + 8

Expand

10 x + 30 - 5 (x - 1) : 5 x + 35

- 160 x^{2} + 116 x + 8 = 5 x + 35

Move

35

to the left side

- 160 x^{2} + 116 x - 27 = 5 x

Move

5 x

to the left side

- 160 x^{2} + 111 x - 27 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 111 \pm 11 1 ^{2} - 4 ( - 160 ) ( - 27 )}{2 ( - 160 )}

Simplify

11 1^{2} - 4 (- 160) (- 27) : 3551 i

x_{1, 2} = \frac{- 111 \pm 3 551 i}{2 ( - 160 )}

Separate the solutions

x_{1} = \frac{- 111 + 3 551 i}{2 ( - 160 )}, x_{2} = \frac{- 111 - 3 551 i}{2 ( - 160 )}

x = \frac{- 111 + 3 551 i}{2 ( - 160 )} : \frac{111}{320} - i \frac{3 551}{320}

x = \frac{- 111 - 3 551 i}{2 ( - 160 )} : \frac{111}{320} + i \frac{3 551}{320}

The solutions to the quadratic equation are:

x = \frac{111}{320} - i \frac{3 551}{320}, x = \frac{111}{320} + i \frac{3 551}{320}

Popular Examples

4 x + 3 = 2 (5 + 2 x)

∣ 4 - 5 x ∣ \leq 19

2 x < 6

(x - 4) (x + 5) = 0

simplify 1/2*8*10 simplify

\frac{1}{2} \cdot 8 \cdot 10