What are the solutions to the equation 4x(x-6)=7 ?

The solutions to the equation 4x(x-6)=7 are x=(6+sqrt(43))/2 ,x=(6-sqrt(43))/2

Find the zeros of 4x(x-6)=7

The zeros of 4x(x-6)=7 are x=(6+sqrt(43))/2 ,x=(6-sqrt(43))/2

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4 x (x - 6) = 7

x = \frac{6 + 43}{2}, x = \frac{6 - 43}{2}

Decimal Notation

x = 6.27871 \dots, x = - 0.27871 \dots

Solution steps

4 x (x - 6) = 7

Expand

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

4 x^{2} - 24 x = 7

Move

7

to the left side

4 x^{2} - 24 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 4 ( - 7 )}{2 \cdot 4}

(- 24)^{2} - 4 \cdot 4 (- 7) = 443

x_{1, 2} = \frac{- ( - 24 ) \pm 4 43}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 4 43}{2 \cdot 4}, x_{2} = \frac{- ( - 24 ) - 4 43}{2 \cdot 4}

x = \frac{- ( - 24 ) + 4 43}{2 \cdot 4} : \frac{6 + 43}{2}

x = \frac{- ( - 24 ) - 4 43}{2 \cdot 4} : \frac{6 - 43}{2}

The solutions to the quadratic equation are:

x = \frac{6 + 43}{2}, x = \frac{6 - 43}{2}

2 x^{2} = 10 x + 48

x, x^{2} - 2 x - 5 = 0

10 x^{2} - 6 = 11 x

(x + 8) (x - 4) = 0

81 r^{2} - 3 = 0

What are the solutions to the equation 4x(x-6)=7 ?
The solutions to the equation 4x(x-6)=7 are x=(6+sqrt(43))/2 ,x=(6-sqrt(43))/2
Find the zeros of 4x(x-6)=7
The zeros of 4x(x-6)=7 are x=(6+sqrt(43))/2 ,x=(6-sqrt(43))/2