What are the solutions to the equation 3x^2+1=5x ?

The solutions to the equation 3x^2+1=5x are x=(5+sqrt(13))/6 ,x=(5-sqrt(13))/6

Find the zeros of 3x^2+1=5x

The zeros of 3x^2+1=5x are x=(5+sqrt(13))/6 ,x=(5-sqrt(13))/6

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3 x^{2} + 1 = 5 x

x = \frac{5 + 13}{6}, x = \frac{5 - 13}{6}

Solution steps

3 x^{2} + 1 = 5 x

Move

5 x

to the left side

3 x^{2} + 1 - 5 x = 0

Write in the standard form

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

3 x^{2} - 5 x + 1 = 0

Solve with the quadratic formula

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

(- 5)^{2} - 4 \cdot 3 \cdot 1 = 13

x_{1, 2} = \frac{- ( - 5 ) \pm 13}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 13}{2 \cdot 3}, x_{2} = \frac{- ( - 5 ) - 13}{2 \cdot 3}

x = \frac{- ( - 5 ) + 13}{2 \cdot 3} : \frac{5 + 13}{6}

x = \frac{- ( - 5 ) - 13}{2 \cdot 3} : \frac{5 - 13}{6}

The solutions to the quadratic equation are:

x = \frac{5 + 13}{6}, x = \frac{5 - 13}{6}

(x + 2)^{2} = x^{2} + 4

5 + 2 ∣ 5 - 4 x ∣ = 11

x^{2} + 10 x + 10 = 0

\frac{64 - 2 ab}{( a - 8 ) ^{2}} + \frac{2 ab - a ^{2}}{( 8 - a ) ^{2}}

2 \cdot \frac{1}{3}

What are the solutions to the equation 3x^2+1=5x ?
The solutions to the equation 3x^2+1=5x are x=(5+sqrt(13))/6 ,x=(5-sqrt(13))/6
Find the zeros of 3x^2+1=5x
The zeros of 3x^2+1=5x are x=(5+sqrt(13))/6 ,x=(5-sqrt(13))/6