What is the answer to (8x^2-2+3x)/(2x-1)=4x ?

The answer to (8x^2-2+3x)/(2x-1)=4x is x= 2/7

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(8x^2-2+3x)/(2x-1)=4x

\frac{8 x ^{2} - 2 + 3 x}{2 x - 1} = 4 x

x = \frac{2}{7}

Decimal Notation

x = 0.28571 \dots

Solution steps

\frac{8 x ^{2} - 2 + 3 x}{2 x - 1} = 4 x

Multiply both sides by

2 x - 1

8 x^{2} - 2 + 3 x = 4 x (2 x - 1)

Expand

4 x (2 x - 1) : 8 x^{2} - 4 x

8 x^{2} - 2 + 3 x = 8 x^{2} - 4 x

Move

2

to the right side

8 x^{2} + 3 x = 8 x^{2} - 4 x + 2

Subtract

8 x^{2} - 4 x

from both sides

8 x^{2} + 3 x - (8 x^{2} - 4 x) = 8 x^{2} - 4 x + 2 - (8 x^{2} - 4 x)

Simplify

7 x = 2

Divide both sides by

7

x = \frac{2}{7}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{2}

Combine undefined points with solutions:

x = \frac{2}{7}

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

\frac{2}{x ^{3}} = 0

\frac{3}{16 y} = \frac{1}{y + 13}

\frac{2}{3 x + 4} - 1 = \frac{5}{2}

4 - \frac{3}{x} = 6 - \frac{5}{x}

What is the answer to (8x^2-2+3x)/(2x-1)=4x ?
The answer to (8x^2-2+3x)/(2x-1)=4x is x= 2/7
Solve for x: (8x^2-2+3x)/(2x-1)=4x
The solution is x= 2/7