What are the solutions to the equation (2(2/3)-1)x^2+4x+2=0 ?

The solutions to the equation (2(2/3)-1)x^2+4x+2=0 are x=sqrt(30)-6,x=-6-sqrt(30)

Find the zeros of (2(2/3)-1)x^2+4x+2=0

The zeros of (2(2/3)-1)x^2+4x+2=0 are x=sqrt(30)-6,x=-6-sqrt(30)

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(2 (\frac{2}{3}) - 1) x^{2} + 4 x + 2 = 0

x = 30 - 6, x = - 6 - 30

Decimal Notation

x = - 0.52277 \dots, x = - 11.47722 \dots

Solution steps

(2 (\frac{2}{3}) - 1) x^{2} + 4 x + 2 = 0

Expand

(2 (\frac{2}{3}) - 1) x^{2} + 4 x + 2 : \frac{1}{3} x^{2} + 4 x + 2

\frac{1}{3} x^{2} + 4 x + 2 = 0

Write in the standard form

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

\frac{x ^{2}}{3} + 4 x + 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot \frac{1}{3} \cdot 2}{2 \cdot \frac{1}{3}}

4^{2} - 4 \cdot \frac{1}{3} \cdot 2 = \frac{2 10}{3}

x_{1, 2} = \frac{- 4 \pm \frac{2 10}{3}}{2 \cdot \frac{1}{3}}

Separate the solutions

x_{1} = \frac{- 4 + \frac{2 10}{3}}{2 \cdot \frac{1}{3}}, x_{2} = \frac{- 4 - \frac{2 10}{3}}{2 \cdot \frac{1}{3}}

x = \frac{- 4 + \frac{2 10}{3}}{2 \frac{1}{3}} : 30 - 6

x = \frac{- 4 - \frac{2 10}{3}}{2 \frac{1}{3}} : - 6 - 30

The solutions to the quadratic equation are:

x = 30 - 6, x = - 6 - 30

x^{2} + 48 x - 1024 = 0

x^{2} - 6 x + 20

h^{2} + 5 h - 155 = 0

c^{2} - 7 c = 0

X^{2} - X + 1 = 0

What are the solutions to the equation (2(2/3)-1)x^2+4x+2=0 ?
The solutions to the equation (2(2/3)-1)x^2+4x+2=0 are x=sqrt(30)-6,x=-6-sqrt(30)
Find the zeros of (2(2/3)-1)x^2+4x+2=0
The zeros of (2(2/3)-1)x^2+4x+2=0 are x=sqrt(30)-6,x=-6-sqrt(30)