Question

Solve for x: 2 over 5 (x − 4) = 2x.

Answer 1

x=-1

Explanation:

2/5(x-4)=2x

Multiply both sides by 5

2(x-4) = 10x

2x-8=10x

-8=8x

-1=x

Check :

2/5(-1-4) = 2*-1

2(-1-4)= -10

-10 = -10

Answer 2

For this case we must solve the following equation:

`\frac {2} {5 (x-4)} = 2x\\\frac {2} {5x-20)} = 2x`

We multiply on both sides by 5x-20:

`2 = 2x (5x-20)\\2 = 10x ^ 2-40x\\-10x ^ 2 + 40x + 2 = 0\\-5x ^ 2 + 20x + 1 = 0`

We apply the quadratic formula:

`x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}`

Where:

`a = -5\\b = 20\\c = 1`

So:

`x = \frac {-20 \pm \sqrt {20 ^ 2-4 (-5) (1)}} {2 (-5)}\\x = \frac {-20 \pm \sqrt {400 + 20}} {- 10}\\x = \frac {-20 \pm \sqrt {420}} {- 10}\\x = \frac {-20 \pm \sqrt {4 * 105}} {- 10}\\x = \frac {-20 \pm2 \sqrt {105}} {- 10}`

Thus, we have two roots:

`x_ {1} = \frac {-10+ \sqrt {105}} {- 5} = \frac {10- \sqrt {105}} {5}\\x_ {2} = \frac {-10- \sqrt {105}} {- 5} = \frac {10+ \sqrt {105}} {5}`

Answer:

`x_ {1} = \frac {10- \sqrt {105}} {5}\\x_ {2} = \frac {10+ \sqrt {105}} {5}`