What are the solutions to the equation x(5x-7)=1 ?

The solutions to the equation x(5x-7)=1 are x=(7+sqrt(69))/(10),x=(7-sqrt(69))/(10)

Find the zeros of x(5x-7)=1

The zeros of x(5x-7)=1 are x=(7+sqrt(69))/(10),x=(7-sqrt(69))/(10)

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x (5 x - 7) = 1

x = \frac{7 + 69}{10}, x = \frac{7 - 69}{10}

Decimal Notation

x = 1.53066 \dots, x = - 0.13066 \dots

Solution steps

x (5 x - 7) = 1

Expand

x (5 x - 7) : 5 x^{2} - 7 x

5 x^{2} - 7 x = 1

Move

1

to the left side

5 x^{2} - 7 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 5 ( - 1 )}{2 \cdot 5}

(- 7)^{2} - 4 \cdot 5 (- 1) = 69

x_{1, 2} = \frac{- ( - 7 ) \pm 69}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 7 ) + 69}{2 \cdot 5}, x_{2} = \frac{- ( - 7 ) - 69}{2 \cdot 5}

x = \frac{- ( - 7 ) + 69}{2 \cdot 5} : \frac{7 + 69}{10}

x = \frac{- ( - 7 ) - 69}{2 \cdot 5} : \frac{7 - 69}{10}

The solutions to the quadratic equation are:

x = \frac{7 + 69}{10}, x = \frac{7 - 69}{10}

\frac{1}{7} \cdot \frac{1}{2}

3 x^{2} + 7 x - 1 = 0

p^{2} + 6 p + 8 = 0

d^{2} + 7 d + 10 = 0

2 x^{3} - 5 x^{2} - 3 x \geq 0

What are the solutions to the equation x(5x-7)=1 ?
The solutions to the equation x(5x-7)=1 are x=(7+sqrt(69))/(10),x=(7-sqrt(69))/(10)
Find the zeros of x(5x-7)=1
The zeros of x(5x-7)=1 are x=(7+sqrt(69))/(10),x=(7-sqrt(69))/(10)