What are the solutions to the equation 3x^2+5=11x ?

The solutions to the equation 3x^2+5=11x are x=(11+sqrt(61))/6 ,x=(11-sqrt(61))/6

Find the zeros of 3x^2+5=11x

The zeros of 3x^2+5=11x are x=(11+sqrt(61))/6 ,x=(11-sqrt(61))/6

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3 x^{2} + 5 = 11 x

x = \frac{11 + 61}{6}, x = \frac{11 - 61}{6}

Decimal Notation

x = 3.13504 \dots, x = 0.53162 \dots

Solution steps

3 x^{2} + 5 = 11 x

Move

11 x

to the left side

3 x^{2} + 5 - 11 x = 0

Write in the standard form

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

3 x^{2} - 11 x + 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 11 ) \pm ( - 11 ) ^{2} - 4 \cdot 3 \cdot 5}{2 \cdot 3}

(- 11)^{2} - 4 \cdot 3 \cdot 5 = 61

x_{1, 2} = \frac{- ( - 11 ) \pm 61}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 11 ) + 61}{2 \cdot 3}, x_{2} = \frac{- ( - 11 ) - 61}{2 \cdot 3}

x = \frac{- ( - 11 ) + 61}{2 \cdot 3} : \frac{11 + 61}{6}

x = \frac{- ( - 11 ) - 61}{2 \cdot 3} : \frac{11 - 61}{6}

The solutions to the quadratic equation are:

x = \frac{11 + 61}{6}, x = \frac{11 - 61}{6}

(\frac{25}{2})^{2}

lo g_{\frac{1}{2}} (\frac{1 - x}{2 - x}) < 0

3 x^{2} = 108

25 x^{4} - 36

5 x^{2} - 7 x - 6 = - 10 x - 4

What are the solutions to the equation 3x^2+5=11x ?
The solutions to the equation 3x^2+5=11x are x=(11+sqrt(61))/6 ,x=(11-sqrt(61))/6
Find the zeros of 3x^2+5=11x
The zeros of 3x^2+5=11x are x=(11+sqrt(61))/6 ,x=(11-sqrt(61))/6