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

The solutions to the equation 4x(x-4)=7 are x=(4+sqrt(23))/2 ,x=(4-sqrt(23))/2

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

The zeros of 4x(x-4)=7 are x=(4+sqrt(23))/2 ,x=(4-sqrt(23))/2

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4 x (x - 4) = 7

x = \frac{4 + 23}{2}, x = \frac{4 - 23}{2}

Decimal Notation

x = 4.39791 \dots, x = - 0.39791 \dots

Solution steps

4 x (x - 4) = 7

Expand

4 x (x - 4) : 4 x^{2} - 16 x

4 x^{2} - 16 x = 7

Move

7

to the left side

4 x^{2} - 16 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 16 ) \pm ( - 16 ) ^{2} - 4 \cdot 4 ( - 7 )}{2 \cdot 4}

(- 16)^{2} - 4 \cdot 4 (- 7) = 423

x_{1, 2} = \frac{- ( - 16 ) \pm 4 23}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 16 ) + 4 23}{2 \cdot 4}, x_{2} = \frac{- ( - 16 ) - 4 23}{2 \cdot 4}

x = \frac{- ( - 16 ) + 4 23}{2 \cdot 4} : \frac{4 + 23}{2}

x = \frac{- ( - 16 ) - 4 23}{2 \cdot 4} : \frac{4 - 23}{2}

The solutions to the quadratic equation are:

x = \frac{4 + 23}{2}, x = \frac{4 - 23}{2}

- 15 t^{2} + 2 = - 7 t

(x - 4) (x + 6) - (x - 3) 2 = 15

\frac{1}{3} x - 4 = x^{2}

3 x^{2} - 15 = 9

x^{2} - 3 x - 4 = - 2

What are the solutions to the equation 4x(x-4)=7 ?
The solutions to the equation 4x(x-4)=7 are x=(4+sqrt(23))/2 ,x=(4-sqrt(23))/2
Find the zeros of 4x(x-4)=7
The zeros of 4x(x-4)=7 are x=(4+sqrt(23))/2 ,x=(4-sqrt(23))/2