What are the solutions to the equation x(3x-4)=-1 ?

The solutions to the equation x(3x-4)=-1 are x=1,x= 1/3

Find the zeros of x(3x-4)=-1

The zeros of x(3x-4)=-1 are x=1,x= 1/3

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x (3 x - 4) = - 1

x = 1, x = \frac{1}{3}

Decimal Notation

x = 1, x = 0.33333 \dots

Solution steps

x (3 x - 4) = - 1

Expand

x (3 x - 4) : 3 x^{2} - 4 x

3 x^{2} - 4 x = - 1

Move

1

to the left side

3 x^{2} - 4 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 3 \cdot 1}{2 \cdot 3}

(- 4)^{2} - 4 \cdot 3 \cdot 1 = 2

x_{1, 2} = \frac{- ( - 4 ) \pm 2}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2}{2 \cdot 3}, x_{2} = \frac{- ( - 4 ) - 2}{2 \cdot 3}

x = \frac{- ( - 4 ) + 2}{2 \cdot 3} : 1

x = \frac{- ( - 4 ) - 2}{2 \cdot 3} : \frac{1}{3}

The solutions to the quadratic equation are:

x = 1, x = \frac{1}{3}

(x + 4) (x - 7) = - 30

x, 2 y - x^{2} = x y

y, 2 x y + 5 y^{2} = 4

5 t^{2} + 14 t - 3 = 0

100 = (x - 1) (200 - 40 x)

What are the solutions to the equation x(3x-4)=-1 ?
The solutions to the equation x(3x-4)=-1 are x=1,x= 1/3
Find the zeros of x(3x-4)=-1
The zeros of x(3x-4)=-1 are x=1,x= 1/3