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

The answer to 3/(2-z)=2z+7 is z=-(3+sqrt(97))/4 ,z=(sqrt(97)-3)/4

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

The solution is z=-(3+sqrt(97))/4 ,z=(sqrt(97)-3)/4

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

z = - \frac{3 + 97}{4}, z = \frac{97 - 3}{4}

Decimal Notation

z = - 3.21221 \dots, z = 1.71221 \dots

Solution steps

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

Multiply both sides by

2 - z

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

Solve

3 = 2 z (2 - z) + 7 (2 - z) : z = - \frac{3 + 97}{4}, z = \frac{97 - 3}{4}

z = - \frac{3 + 97}{4}, z = \frac{97 - 3}{4}

Verify Solutions

Find undefined (singularity) points:

z = 2

Combine undefined points with solutions:

z = - \frac{3 + 97}{4}, z = \frac{97 - 3}{4}

\frac{1000 p - 5400}{1000 p} = 0.25

\frac{8}{x} = - 6

a = (\frac{b}{x}) + x

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

A, \frac{b + c}{A} = 3

What is the answer to 3/(2-z)=2z+7 ?
The answer to 3/(2-z)=2z+7 is z=-(3+sqrt(97))/4 ,z=(sqrt(97)-3)/4
Solve for z: 3/(2-z)=2z+7
The solution is z=-(3+sqrt(97))/4 ,z=(sqrt(97)-3)/4