What are the solutions to the equation 3x^2=11x-4 ?

The solutions to the equation 3x^2=11x-4 are x=(11+sqrt(73))/6 ,x=(11-sqrt(73))/6

Find the zeros of 3x^2=11x-4

The zeros of 3x^2=11x-4 are x=(11+sqrt(73))/6 ,x=(11-sqrt(73))/6

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3 x^{2} = 11 x - 4

x = \frac{11 + 73}{6}, x = \frac{11 - 73}{6}

Solution steps

3 x^{2} = 11 x - 4

Move

4

to the left side

3 x^{2} + 4 = 11 x

Move

11 x

to the left side

3 x^{2} + 4 - 11 x = 0

Write in the standard form

a x^{2} + b x + c = 0

3 x^{2} - 11 x + 4 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 11 ) \pm ( - 11 ) ^{2} - 4 \cdot 3 \cdot 4}{2 \cdot 3}

(- 11)^{2} - 4 \cdot 3 \cdot 4 = 73

x_{1, 2} = \frac{- ( - 11 ) \pm 73}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 11 ) + 73}{2 \cdot 3}, x_{2} = \frac{- ( - 11 ) - 73}{2 \cdot 3}

x = \frac{- ( - 11 ) + 73}{2 \cdot 3} : \frac{11 + 73}{6}

x = \frac{- ( - 11 ) - 73}{2 \cdot 3} : \frac{11 - 73}{6}

The solutions to the quadratic equation are:

x = \frac{11 + 73}{6}, x = \frac{11 - 73}{6}

g^{2} + g = 56

7 x^{2} - 6 = 0

9 x^{2} + 17 x + 8 = 0

16 x^{2} - 8 x t - 3 t^{2}

x + 2 = 6 x - 18

What are the solutions to the equation 3x^2=11x-4 ?
The solutions to the equation 3x^2=11x-4 are x=(11+sqrt(73))/6 ,x=(11-sqrt(73))/6
Find the zeros of 3x^2=11x-4
The zeros of 3x^2=11x-4 are x=(11+sqrt(73))/6 ,x=(11-sqrt(73))/6