What is the answer to 5/(2+sqrt(x))= 13/6 ?

The answer to 5/(2+sqrt(x))= 13/6 is x= 16/169

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5/(2+sqrt(x))= 13/6

\frac{5}{2 + x} = \frac{13}{6}

x = \frac{16}{169}

Decimal Notation

x = 0.09467 \dots

Solution steps

\frac{5}{2 + x} = \frac{13}{6}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

5 \cdot 6 = (2 + x) \cdot 13

Expand

(2 + x) \cdot 13 : 26 + 13 x

5 \cdot 6 = 26 + 13 x

Switch sides

26 + 13 x = 5 \cdot 6

Multiply the numbers:

5 \cdot 6 = 30

26 + 13 x = 30

Move

26

to the right side

13 x = 4

Divide both sides by

13

x = \frac{4}{13}

Square both sides:

x = \frac{16}{169}

x = \frac{16}{169}

Verify Solutions:

x = \frac{16}{169}

True

The solution is

x = \frac{16}{169}

2 x + 1 = x - 1

x^{2} - 2 x + 2 = 0

\frac{( 2 x - 3 )}{( x - 1 )} = 2

0.8 = (\frac{1}{0.018}) [(1.63)]^{0.67} (s)^{\frac{1}{2}}

32 - x \cdot 15 = 27 + 5

What is the answer to 5/(2+sqrt(x))= 13/6 ?
The answer to 5/(2+sqrt(x))= 13/6 is x= 16/169
Solve for x: 5/(2+sqrt(x))= 13/6
The solution is x= 16/169