What are the solutions to the equation 4x(x-6)=5 ?

The solutions to the equation 4x(x-6)=5 are x=(6+sqrt(41))/2 ,x=(6-sqrt(41))/2

Find the zeros of 4x(x-6)=5

The zeros of 4x(x-6)=5 are x=(6+sqrt(41))/2 ,x=(6-sqrt(41))/2

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4 x (x - 6) = 5

x = \frac{6 + 41}{2}, x = \frac{6 - 41}{2}

Solution steps

4 x (x - 6) = 5

Expand

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

4 x^{2} - 24 x = 5

Move

5

to the left side

4 x^{2} - 24 x - 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 4 ( - 5 )}{2 \cdot 4}

(- 24)^{2} - 4 \cdot 4 (- 5) = 441

x_{1, 2} = \frac{- ( - 24 ) \pm 4 41}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 4 41}{2 \cdot 4}, x_{2} = \frac{- ( - 24 ) - 4 41}{2 \cdot 4}

x = \frac{- ( - 24 ) + 4 41}{2 \cdot 4} : \frac{6 + 41}{2}

x = \frac{- ( - 24 ) - 4 41}{2 \cdot 4} : \frac{6 - 41}{2}

The solutions to the quadratic equation are:

x = \frac{6 + 41}{2}, x = \frac{6 - 41}{2}

4 x (x - 6) = 7

2 x^{2} = 10 x + 48

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

10 x^{2} - 6 = 11 x

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

What are the solutions to the equation 4x(x-6)=5 ?
The solutions to the equation 4x(x-6)=5 are x=(6+sqrt(41))/2 ,x=(6-sqrt(41))/2
Find the zeros of 4x(x-6)=5
The zeros of 4x(x-6)=5 are x=(6+sqrt(41))/2 ,x=(6-sqrt(41))/2