What are the solutions to the equation 24x(x+1)=4x^2-7 ?

The solutions to the equation 24x(x+1)=4x^2-7 are x=-1/2 ,x=-7/10

Find the zeros of 24x(x+1)=4x^2-7

The zeros of 24x(x+1)=4x^2-7 are x=-1/2 ,x=-7/10

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24 x (x + 1) = 4 x^{2} - 7

x = - \frac{1}{2}, x = - \frac{7}{10}

Decimal Notation

x = - 0.5, x = - 0.7

Solution steps

24 x (x + 1) = 4 x^{2} - 7

Expand

24 x (x + 1) : 24 x^{2} + 24 x

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

Move

7

to the left side

24 x^{2} + 24 x + 7 = 4 x^{2}

Move

4 x^{2}

to the left side

20 x^{2} + 24 x + 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 24 \pm 2 4 ^{2} - 4 \cdot 20 \cdot 7}{2 \cdot 20}

2 4^{2} - 4 \cdot 20 \cdot 7 = 4

x_{1, 2} = \frac{- 24 \pm 4}{2 \cdot 20}

Separate the solutions

x_{1} = \frac{- 24 + 4}{2 \cdot 20}, x_{2} = \frac{- 24 - 4}{2 \cdot 20}

x = \frac{- 24 + 4}{2 \cdot 20} : - \frac{1}{2}

x = \frac{- 24 - 4}{2 \cdot 20} : - \frac{7}{10}

The solutions to the quadratic equation are:

x = - \frac{1}{2}, x = - \frac{7}{10}

4 x^{2} - 11 = 4 x

4 (x^{2} - 7) - 10 = - 13

28 q^{2} + 90 q = 0

3 x^{2} = 3 x + 5

x^{2} + 16 = - 8 x

What are the solutions to the equation 24x(x+1)=4x^2-7 ?
The solutions to the equation 24x(x+1)=4x^2-7 are x=-1/2 ,x=-7/10
Find the zeros of 24x(x+1)=4x^2-7
The zeros of 24x(x+1)=4x^2-7 are x=-1/2 ,x=-7/10