What are the solutions to the equation 4x^2-9=-6x ?

The solutions to the equation 4x^2-9=-6x are x=(3(sqrt(5)-1))/4 ,x=-(3(1+sqrt(5)))/4

Find the zeros of 4x^2-9=-6x

The zeros of 4x^2-9=-6x are x=(3(sqrt(5)-1))/4 ,x=-(3(1+sqrt(5)))/4

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4 x^{2} - 9 = - 6 x

x = \frac{3 ( 5 - 1 )}{4}, x = - \frac{3 ( 1 + 5 )}{4}

Decimal Notation

x = 0.92705 \dots, x = - 2.42705 \dots

Solution steps

4 x^{2} - 9 = - 6 x

Move

6 x

to the left side

4 x^{2} - 9 + 6 x = 0

Write in the standard form

a x^{2} + b x + c = 0

4 x^{2} + 6 x - 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 4 ( - 9 )}{2 \cdot 4}

6^{2} - 4 \cdot 4 (- 9) = 65

x_{1, 2} = \frac{- 6 \pm 6 5}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- 6 + 6 5}{2 \cdot 4}, x_{2} = \frac{- 6 - 6 5}{2 \cdot 4}

x = \frac{- 6 + 6 5}{2 \cdot 4} : \frac{3 ( 5 - 1 )}{4}

x = \frac{- 6 - 6 5}{2 \cdot 4} : - \frac{3 ( 1 + 5 )}{4}

The solutions to the quadratic equation are:

x = \frac{3 ( 5 - 1 )}{4}, x = - \frac{3 ( 1 + 5 )}{4}

\frac{1}{2} x^{2} + 2 x + 3 = 0

4 x^{2} + 25 x + 8 = 0

x \cdot 2 x = 4 \cdot 13

x^{2} + 1 = 0

(2 x + 3) (x + 4) = 67

What are the solutions to the equation 4x^2-9=-6x ?
The solutions to the equation 4x^2-9=-6x are x=(3(sqrt(5)-1))/4 ,x=-(3(1+sqrt(5)))/4
Find the zeros of 4x^2-9=-6x
The zeros of 4x^2-9=-6x are x=(3(sqrt(5)-1))/4 ,x=-(3(1+sqrt(5)))/4