What are the solutions to the equation 3x^2-12x+11=x ?

The solutions to the equation 3x^2-12x+11=x are x=(13+sqrt(37))/6 ,x=(13-sqrt(37))/6

Find the zeros of 3x^2-12x+11=x

The zeros of 3x^2-12x+11=x are x=(13+sqrt(37))/6 ,x=(13-sqrt(37))/6

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3 x^{2} - 12 x + 11 = x

x = \frac{13 + 37}{6}, x = \frac{13 - 37}{6}

Decimal Notation

x = 3.18046 \dots, x = 1.15287 \dots

Solution steps

3 x^{2} - 12 x + 11 = x

Move

x

to the left side

3 x^{2} - 13 x + 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 13 ) \pm ( - 13 ) ^{2} - 4 \cdot 3 \cdot 11}{2 \cdot 3}

(- 13)^{2} - 4 \cdot 3 \cdot 11 = 37

x_{1, 2} = \frac{- ( - 13 ) \pm 37}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 13 ) + 37}{2 \cdot 3}, x_{2} = \frac{- ( - 13 ) - 37}{2 \cdot 3}

x = \frac{- ( - 13 ) + 37}{2 \cdot 3} : \frac{13 + 37}{6}

x = \frac{- ( - 13 ) - 37}{2 \cdot 3} : \frac{13 - 37}{6}

The solutions to the quadratic equation are:

x = \frac{13 + 37}{6}, x = \frac{13 - 37}{6}

lo g_{4} (32) + lo g_{4} (2)

5 x = 45

\frac{3 x - 8}{2} = 5

\frac{9}{10} + \frac{3}{5}

5 x - 9 = 0

What are the solutions to the equation 3x^2-12x+11=x ?
The solutions to the equation 3x^2-12x+11=x are x=(13+sqrt(37))/6 ,x=(13-sqrt(37))/6
Find the zeros of 3x^2-12x+11=x
The zeros of 3x^2-12x+11=x are x=(13+sqrt(37))/6 ,x=(13-sqrt(37))/6