What is the answer to (2q)/(10-3q)=10-3q ?

The answer to (2q)/(10-3q)=10-3q is q=(31+sqrt(61))/9 ,q=(31-sqrt(61))/9

Solve for q: (2q)/(10-3q)=10-3q

The solution is q=(31+sqrt(61))/9 ,q=(31-sqrt(61))/9

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\frac{2 q}{10 - 3 q} = 10 - 3 q

q = \frac{31 + 61}{9}, q = \frac{31 - 61}{9}

Decimal Notation

q = 4.31224 \dots, q = 2.57663 \dots

Solution steps

\frac{2 q}{10 - 3 q} = 10 - 3 q

Multiply both sides by

10 - 3 q

2 q = 10 (10 - 3 q) - 3 q (10 - 3 q)

Solve

2 q = 10 (10 - 3 q) - 3 q (10 - 3 q) : q = \frac{31 + 61}{9}, q = \frac{31 - 61}{9}

q = \frac{31 + 61}{9}, q = \frac{31 - 61}{9}

Verify Solutions

Find undefined (singularity) points:

q = \frac{10}{3}

Combine undefined points with solutions:

q = \frac{31 + 61}{9}, q = \frac{31 - 61}{9}

2 x = \frac{1}{2 x}

\frac{1}{x} = 8

\frac{4}{x} = \frac{5}{10}

\frac{x}{3 ^{2} - x} = 2^{2}

4 + \frac{6}{y - 3} = \frac{2 y}{y - 3}

What is the answer to (2q)/(10-3q)=10-3q ?
The answer to (2q)/(10-3q)=10-3q is q=(31+sqrt(61))/9 ,q=(31-sqrt(61))/9
Solve for q: (2q)/(10-3q)=10-3q
The solution is q=(31+sqrt(61))/9 ,q=(31-sqrt(61))/9