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

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

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

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

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

x = 3 + 23, x = 3 - 23

Decimal Notation

x = 6.46410 \dots, x = - 0.46410 \dots

Solution steps

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

Move

2 x

to the left side

x^{2} - 6 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot ( - 3 )}{2 \cdot 1}

(- 6)^{2} - 4 \cdot 1 \cdot (- 3) = 43

x_{1, 2} = \frac{- ( - 6 ) \pm 4 3}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 4 3}{2 \cdot 1}, x_{2} = \frac{- ( - 6 ) - 4 3}{2 \cdot 1}

x = \frac{- ( - 6 ) + 4 3}{2 \cdot 1} : 3 + 23

x = \frac{- ( - 6 ) - 4 3}{2 \cdot 1} : 3 - 23

The solutions to the quadratic equation are:

x = 3 + 23, x = 3 - 23

- 4.9 t^{2} + 24.5 t + 2 = 0

x^{2} + 1 + x = 0

3 x^{2} - 14 x + 4 = 4

a^{2} = 20

a^{2} = 11

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