What are the solutions to the equation 3r^2=4r-1 ?

The solutions to the equation 3r^2=4r-1 are r=1,r= 1/3

Find the zeros of 3r^2=4r-1

The zeros of 3r^2=4r-1 are r=1,r= 1/3

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3 r^{2} = 4 r - 1

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

Decimal Notation

r = 1, r = 0.33333 \dots

Solution steps

3 r^{2} = 4 r - 1

Move

1

to the left side

3 r^{2} + 1 = 4 r

Move

4 r

to the left side

3 r^{2} + 1 - 4 r = 0

Write in the standard form

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

3 r^{2} - 4 r + 1 = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

z^{2} + 4 z + 1 = 0

x^{2} + 7 x - 9 = 0

(x + 5) (2 x - 1) = 0

- t^{2} + 2 t + 3 = 0

2 x^{2} - 6 x = - 1

What are the solutions to the equation 3r^2=4r-1 ?
The solutions to the equation 3r^2=4r-1 are r=1,r= 1/3
Find the zeros of 3r^2=4r-1
The zeros of 3r^2=4r-1 are r=1,r= 1/3