What are the solutions to the equation x(2x-11)=12 ?

The solutions to the equation x(2x-11)=12 are x=(11+sqrt(217))/4 ,x=(11-sqrt(217))/4

Find the zeros of x(2x-11)=12

The zeros of x(2x-11)=12 are x=(11+sqrt(217))/4 ,x=(11-sqrt(217))/4

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x (2 x - 11) = 12

x = \frac{11 + 217}{4}, x = \frac{11 - 217}{4}

Decimal Notation

x = 6.43272 \dots, x = - 0.93272 \dots

Solution steps

x (2 x - 11) = 12

Expand

x (2 x - 11) : 2 x^{2} - 11 x

2 x^{2} - 11 x = 12

Move

12

to the left side

2 x^{2} - 11 x - 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 11 ) \pm ( - 11 ) ^{2} - 4 \cdot 2 ( - 12 )}{2 \cdot 2}

(- 11)^{2} - 4 \cdot 2 (- 12) = 217

x_{1, 2} = \frac{- ( - 11 ) \pm 217}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 11 ) + 217}{2 \cdot 2}, x_{2} = \frac{- ( - 11 ) - 217}{2 \cdot 2}

x = \frac{- ( - 11 ) + 217}{2 \cdot 2} : \frac{11 + 217}{4}

x = \frac{- ( - 11 ) - 217}{2 \cdot 2} : \frac{11 - 217}{4}

The solutions to the quadratic equation are:

x = \frac{11 + 217}{4}, x = \frac{11 - 217}{4}

x^{2} - 50 x - 5000 = 0

- 16 x^{2} + 107 x + 63 = 0

r^{2} + 10 r + 22 = 0

2 x^{2} + 15 x - 11 = - 3

21 c^{2} - 16 c - 6 = 1 - 2 c

What are the solutions to the equation x(2x-11)=12 ?
The solutions to the equation x(2x-11)=12 are x=(11+sqrt(217))/4 ,x=(11-sqrt(217))/4
Find the zeros of x(2x-11)=12
The zeros of x(2x-11)=12 are x=(11+sqrt(217))/4 ,x=(11-sqrt(217))/4