What are the solutions to the equation 3r^2-2r-1=0 ?

The solutions to the equation 3r^2-2r-1=0 are r=1,r=-1/3

Find the zeros of 3r^2-2r-1=0

The zeros of 3r^2-2r-1=0 are r=1,r=-1/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3 r^{2} - 2 r - 1 = 0

r = 1, r = - \frac{1}{3}

Decimal Notation

r = 1, r = - 0.33333 \dots

Solution steps

3 r^{2} - 2 r - 1 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 3 ( - 1 )}{2 \cdot 3}

(- 2)^{2} - 4 \cdot 3 (- 1) = 4

r_{1, 2} = \frac{- ( - 2 ) \pm 4}{2 \cdot 3}

Separate the solutions

r_{1} = \frac{- ( - 2 ) + 4}{2 \cdot 3}, r_{2} = \frac{- ( - 2 ) - 4}{2 \cdot 3}

r = \frac{- ( - 2 ) + 4}{2 \cdot 3} : 1

r = \frac{- ( - 2 ) - 4}{2 \cdot 3} : - \frac{1}{3}

The solutions to the quadratic equation are:

r = 1, r = - \frac{1}{3}

(x + 4) (3 x - 7) = 0

- 12 x^{2} + 24 x = 0

x^{2} - 8 x + 5

4 x^{2} - 3 x - 22 = 0

m^{2} - 4 m - 5 = 0

What are the solutions to the equation 3r^2-2r-1=0 ?
The solutions to the equation 3r^2-2r-1=0 are r=1,r=-1/3
Find the zeros of 3r^2-2r-1=0
The zeros of 3r^2-2r-1=0 are r=1,r=-1/3