What is the answer to 3/(2-z)=z+7 ?

The answer to 3/(2-z)=z+7 is z=-(5+sqrt(69))/2 ,z=(sqrt(69)-5)/2

Solve for z: 3/(2-z)=z+7

The solution is z=-(5+sqrt(69))/2 ,z=(sqrt(69)-5)/2

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\frac{3}{2 - z} = z + 7

z = - \frac{5 + 69}{2}, z = \frac{69 - 5}{2}

Decimal Notation

z = - 6.65331 \dots, z = 1.65331 \dots

Solution steps

\frac{3}{2 - z} = z + 7

Multiply both sides by

2 - z

3 = z (2 - z) + 7 (2 - z)

Solve

3 = z (2 - z) + 7 (2 - z) : z = - \frac{5 + 69}{2}, z = \frac{69 - 5}{2}

z = - \frac{5 + 69}{2}, z = \frac{69 - 5}{2}

Verify Solutions

Find undefined (singularity) points:

z = 2

Combine undefined points with solutions:

z = - \frac{5 + 69}{2}, z = \frac{69 - 5}{2}

\frac{3}{x} = \frac{13}{5 x} + 2

\frac{2 x}{x + 6} = \frac{2 x - 6}{x}

\frac{x + 1}{x} + \frac{2}{x - 3} = 1

\frac{2}{x + 1} - \frac{x}{x - 1} = 3

\frac{6}{x} = 2

What is the answer to 3/(2-z)=z+7 ?
The answer to 3/(2-z)=z+7 is z=-(5+sqrt(69))/2 ,z=(sqrt(69)-5)/2
Solve for z: 3/(2-z)=z+7
The solution is z=-(5+sqrt(69))/2 ,z=(sqrt(69)-5)/2