What are the solutions to the equation 14x^2+33x=3x^2+3x+1 ?

The solutions to the equation 14x^2+33x=3x^2+3x+1 are x=-(15+2sqrt(59))/(11),x=(2sqrt(59)-15)/(11)

Find the zeros of 14x^2+33x=3x^2+3x+1

The zeros of 14x^2+33x=3x^2+3x+1 are x=-(15+2sqrt(59))/(11),x=(2sqrt(59)-15)/(11)

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14 x^{2} + 33 x = 3 x^{2} + 3 x + 1

x = - \frac{15 + 2 59}{11}, x = \frac{2 59 - 15}{11}

Decimal Notation

x = - 2.76020 \dots, x = 0.03293 \dots

Solution steps

14 x^{2} + 33 x = 3 x^{2} + 3 x + 1

Switch sides

3 x^{2} + 3 x + 1 = 14 x^{2} + 33 x

Move

33 x

to the left side

3 x^{2} - 30 x + 1 = 14 x^{2}

Move

14 x^{2}

to the left side

- 11 x^{2} - 30 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 30 ) \pm ( - 30 ) ^{2} - 4 ( - 11 ) \cdot 1}{2 ( - 11 )}

(- 30)^{2} - 4 (- 11) \cdot 1 = 459

x_{1, 2} = \frac{- ( - 30 ) \pm 4 59}{2 ( - 11 )}

Separate the solutions

x_{1} = \frac{- ( - 30 ) + 4 59}{2 ( - 11 )}, x_{2} = \frac{- ( - 30 ) - 4 59}{2 ( - 11 )}

x = \frac{- ( - 30 ) + 4 59}{2 ( - 11 )} : - \frac{15 + 2 59}{11}

x = \frac{- ( - 30 ) - 4 59}{2 ( - 11 )} : \frac{2 59 - 15}{11}

The solutions to the quadratic equation are:

x = - \frac{15 + 2 59}{11}, x = \frac{2 59 - 15}{11}

(x + 2)^{2} - 3 = \frac{2 x - 5}{3}

7.9461 x^{2} + 7.2 x - 7.9461 = 0

x, f = x^{2} + 4 k x + (3 + 11 k)

x^{2} - 20 = 25

s^{2} + 4.5 s + 9.1310625 = 0

What are the solutions to the equation 14x^2+33x=3x^2+3x+1 ?
The solutions to the equation 14x^2+33x=3x^2+3x+1 are x=-(15+2sqrt(59))/(11),x=(2sqrt(59)-15)/(11)
Find the zeros of 14x^2+33x=3x^2+3x+1
The zeros of 14x^2+33x=3x^2+3x+1 are x=-(15+2sqrt(59))/(11),x=(2sqrt(59)-15)/(11)