What are the solutions to the equation 2x(x-6)=3 ?

The solutions to the equation 2x(x-6)=3 are x=(6+sqrt(42))/2 ,x=(6-sqrt(42))/2

Find the zeros of 2x(x-6)=3

The zeros of 2x(x-6)=3 are x=(6+sqrt(42))/2 ,x=(6-sqrt(42))/2

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2 x (x - 6) = 3

x = \frac{6 + 42}{2}, x = \frac{6 - 42}{2}

Decimal Notation

x = 6.24037 \dots, x = - 0.24037 \dots

Solution steps

2 x (x - 6) = 3

Expand

2 x (x - 6) : 2 x^{2} - 12 x

2 x^{2} - 12 x = 3

Move

3

to the left side

2 x^{2} - 12 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 2 ( - 3 )}{2 \cdot 2}

(- 12)^{2} - 4 \cdot 2 (- 3) = 242

x_{1, 2} = \frac{- ( - 12 ) \pm 2 42}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 2 42}{2 \cdot 2}, x_{2} = \frac{- ( - 12 ) - 2 42}{2 \cdot 2}

x = \frac{- ( - 12 ) + 2 42}{2 \cdot 2} : \frac{6 + 42}{2}

x = \frac{- ( - 12 ) - 2 42}{2 \cdot 2} : \frac{6 - 42}{2}

The solutions to the quadratic equation are:

x = \frac{6 + 42}{2}, x = \frac{6 - 42}{2}

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

12 x^{2} - 4 = 13 x

(- x + 5)^{2} - 45 = 0

9 x^{2} + 4 x + 5 = 0

x^{2} + 2 x = 15

What are the solutions to the equation 2x(x-6)=3 ?
The solutions to the equation 2x(x-6)=3 are x=(6+sqrt(42))/2 ,x=(6-sqrt(42))/2
Find the zeros of 2x(x-6)=3
The zeros of 2x(x-6)=3 are x=(6+sqrt(42))/2 ,x=(6-sqrt(42))/2