What are the solutions to the equation 4x(x-6)=-9 ?

The solutions to the equation 4x(x-6)=-9 are x=(3(2+sqrt(3)))/2 ,x=(3(2-sqrt(3)))/2

Find the zeros of 4x(x-6)=-9

The zeros of 4x(x-6)=-9 are x=(3(2+sqrt(3)))/2 ,x=(3(2-sqrt(3)))/2

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4 x (x - 6) = - 9

x = \frac{3 ( 2 + 3 )}{2}, x = \frac{3 ( 2 - 3 )}{2}

Decimal Notation

x = 5.59807 \dots, x = 0.40192 \dots

Solution steps

4 x (x - 6) = - 9

Expand

4 x (x - 6) : 4 x^{2} - 24 x

4 x^{2} - 24 x = - 9

Move

9

to the left side

4 x^{2} - 24 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 4 \cdot 9}{2 \cdot 4}

(- 24)^{2} - 4 \cdot 4 \cdot 9 = 123

x_{1, 2} = \frac{- ( - 24 ) \pm 12 3}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 12 3}{2 \cdot 4}, x_{2} = \frac{- ( - 24 ) - 12 3}{2 \cdot 4}

x = \frac{- ( - 24 ) + 12 3}{2 \cdot 4} : \frac{3 ( 2 + 3 )}{2}

x = \frac{- ( - 24 ) - 12 3}{2 \cdot 4} : \frac{3 ( 2 - 3 )}{2}

The solutions to the quadratic equation are:

x = \frac{3 ( 2 + 3 )}{2}, x = \frac{3 ( 2 - 3 )}{2}

3 x^{2} + 26 x + 47 = 7

2 x^{2} + 28 = 100

x^{2} - 20 x + 118 = 0

(x^{2} + 16) = 0

(6 x) (x - 6) = 0

What are the solutions to the equation 4x(x-6)=-9 ?
The solutions to the equation 4x(x-6)=-9 are x=(3(2+sqrt(3)))/2 ,x=(3(2-sqrt(3)))/2
Find the zeros of 4x(x-6)=-9
The zeros of 4x(x-6)=-9 are x=(3(2+sqrt(3)))/2 ,x=(3(2-sqrt(3)))/2