What are the solutions to the equation (4x^2-1)/1 =x(10x-9) ?

The solutions to the equation (4x^2-1)/1 =x(10x-9) are x=(9-sqrt(57))/(12),x=(9+sqrt(57))/(12)

Find the zeros of (4x^2-1)/1 =x(10x-9)

The zeros of (4x^2-1)/1 =x(10x-9) are x=(9-sqrt(57))/(12),x=(9+sqrt(57))/(12)

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\frac{4 x ^{2} - 1}{1} = x (10 x - 9)

x = \frac{9 - 57}{12}, x = \frac{9 + 57}{12}

Decimal Notation

x = 0.12084 \dots, x = 1.37915 \dots

Solution steps

\frac{4 x ^{2} - 1}{1} = x (10 x - 9)

Expand

x (10 x - 9) : 10 x^{2} - 9 x

4 x^{2} - 1 = 10 x^{2} - 9 x

Move

9 x

to the left side

4 x^{2} - 1 + 9 x = 10 x^{2}

Move

10 x^{2}

to the left side

- 6 x^{2} + 9 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 ( - 6 ) ( - 1 )}{2 ( - 6 )}

9^{2} - 4 (- 6) (- 1) = 57

x_{1, 2} = \frac{- 9 \pm 57}{2 ( - 6 )}

Separate the solutions

x_{1} = \frac{- 9 + 57}{2 ( - 6 )}, x_{2} = \frac{- 9 - 57}{2 ( - 6 )}

x = \frac{- 9 + 57}{2 ( - 6 )} : \frac{9 - 57}{12}

x = \frac{- 9 - 57}{2 ( - 6 )} : \frac{9 + 57}{12}

The solutions to the quadratic equation are:

x = \frac{9 - 57}{12}, x = \frac{9 + 57}{12}

11 - 6 w < 5 - 8 w

x^{3} + x^{2} - x \leq 1

- 3 x \leq 21

4 x^{2} + 7 x - 3 = 0

x^{3} + 4 x^{2} - 14 x - 56

What are the solutions to the equation (4x^2-1)/1 =x(10x-9) ?
The solutions to the equation (4x^2-1)/1 =x(10x-9) are x=(9-sqrt(57))/(12),x=(9+sqrt(57))/(12)
Find the zeros of (4x^2-1)/1 =x(10x-9)
The zeros of (4x^2-1)/1 =x(10x-9) are x=(9-sqrt(57))/(12),x=(9+sqrt(57))/(12)