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

The solutions to the equation 3x^2+11=4x are x= 2/3+i(sqrt(29))/3 ,x= 2/3-i(sqrt(29))/3

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

The zeros of 3x^2+11=4x are x= 2/3+i(sqrt(29))/3 ,x= 2/3-i(sqrt(29))/3

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3 x^{2} + 11 = 4 x

x = \frac{2}{3} + i \frac{29}{3}, x = \frac{2}{3} - i \frac{29}{3}

Solution steps

3 x^{2} + 11 = 4 x

Move

4 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

Simplify

(- 4)^{2} - 4 \cdot 3 \cdot 11 : 229 i

x_{1, 2} = \frac{- ( - 4 ) \pm 2 29 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 29 i}{2 \cdot 3}, x_{2} = \frac{- ( - 4 ) - 2 29 i}{2 \cdot 3}

x = \frac{- ( - 4 ) + 2 29 i}{2 \cdot 3} : \frac{2}{3} + i \frac{29}{3}

x = \frac{- ( - 4 ) - 2 29 i}{2 \cdot 3} : \frac{2}{3} - i \frac{29}{3}

The solutions to the quadratic equation are:

x = \frac{2}{3} + i \frac{29}{3}, x = \frac{2}{3} - i \frac{29}{3}

12

- 6 x - 6 = - 6 x - 103

4 x = 76

3 x^{2} + 3 x - 5 = 0

9^{6}

What are the solutions to the equation 3x^2+11=4x ?
The solutions to the equation 3x^2+11=4x are x= 2/3+i(sqrt(29))/3 ,x= 2/3-i(sqrt(29))/3
Find the zeros of 3x^2+11=4x
The zeros of 3x^2+11=4x are x= 2/3+i(sqrt(29))/3 ,x= 2/3-i(sqrt(29))/3