What are the solutions to the equation 4x^2-1=6x ?

The solutions to the equation 4x^2-1=6x are x=(3+sqrt(13))/4 ,x=(3-sqrt(13))/4

Find the zeros of 4x^2-1=6x

The zeros of 4x^2-1=6x are x=(3+sqrt(13))/4 ,x=(3-sqrt(13))/4

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4 x^{2} - 1 = 6 x

x = \frac{3 + 13}{4}, x = \frac{3 - 13}{4}

Decimal Notation

x = 1.65138 \dots, x = - 0.15138 \dots

Solution steps

4 x^{2} - 1 = 6 x

Move

6 x

to the left side

4 x^{2} - 1 - 6 x = 0

Write in the standard form

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

4 x^{2} - 6 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 4 ( - 1 )}{2 \cdot 4}

(- 6)^{2} - 4 \cdot 4 (- 1) = 213

x_{1, 2} = \frac{- ( - 6 ) \pm 2 13}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 13}{2 \cdot 4}, x_{2} = \frac{- ( - 6 ) - 2 13}{2 \cdot 4}

x = \frac{- ( - 6 ) + 2 13}{2 \cdot 4} : \frac{3 + 13}{4}

x = \frac{- ( - 6 ) - 2 13}{2 \cdot 4} : \frac{3 - 13}{4}

The solutions to the quadratic equation are:

x = \frac{3 + 13}{4}, x = \frac{3 - 13}{4}

x, 3 x^{2} - 8 x y + 6 y^{2} - 5 x - 5 y + 20 = 0

x, f = x^{2} - 8 x - m

(m + 5) (m + 2) = 0

8 x^{2} = 16 x

8 x^{2} = 128

What are the solutions to the equation 4x^2-1=6x ?
The solutions to the equation 4x^2-1=6x are x=(3+sqrt(13))/4 ,x=(3-sqrt(13))/4
Find the zeros of 4x^2-1=6x
The zeros of 4x^2-1=6x are x=(3+sqrt(13))/4 ,x=(3-sqrt(13))/4