What are the solutions to the equation 4x^2-3=8x ?

The solutions to the equation 4x^2-3=8x are x=(2+sqrt(7))/2 ,x=(2-sqrt(7))/2

Find the zeros of 4x^2-3=8x

The zeros of 4x^2-3=8x are x=(2+sqrt(7))/2 ,x=(2-sqrt(7))/2

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4 x^{2} - 3 = 8 x

x = \frac{2 + 7}{2}, x = \frac{2 - 7}{2}

Decimal Notation

x = 2.32287 \dots, x = - 0.32287 \dots

Solution steps

4 x^{2} - 3 = 8 x

Move

8 x

to the left side

4 x^{2} - 3 - 8 x = 0

Write in the standard form

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

4 x^{2} - 8 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 4 ( - 3 )}{2 \cdot 4}

(- 8)^{2} - 4 \cdot 4 (- 3) = 47

x_{1, 2} = \frac{- ( - 8 ) \pm 4 7}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 4 7}{2 \cdot 4}, x_{2} = \frac{- ( - 8 ) - 4 7}{2 \cdot 4}

x = \frac{- ( - 8 ) + 4 7}{2 \cdot 4} : \frac{2 + 7}{2}

x = \frac{- ( - 8 ) - 4 7}{2 \cdot 4} : \frac{2 - 7}{2}

The solutions to the quadratic equation are:

x = \frac{2 + 7}{2}, x = \frac{2 - 7}{2}

(y - 3)^{2} - 36

x^{4} - 3 x^{2} - 10

x^{6} - 15 x^{5} - 16 x^{4}

x^{2} - 8 x = 12

8 x y + 6 y - 20 x - 15

What are the solutions to the equation 4x^2-3=8x ?
The solutions to the equation 4x^2-3=8x are x=(2+sqrt(7))/2 ,x=(2-sqrt(7))/2
Find the zeros of 4x^2-3=8x
The zeros of 4x^2-3=8x are x=(2+sqrt(7))/2 ,x=(2-sqrt(7))/2