What are the solutions to the equation 4w^2=4w+3 ?

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

Find the zeros of 4w^2=4w+3

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

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4 w^{2} = 4 w + 3

w = \frac{3}{2}, w = - \frac{1}{2}

Decimal Notation

w = 1.5, w = - 0.5

Solution steps

4 w^{2} = 4 w + 3

Move

3

to the left side

4 w^{2} - 3 = 4 w

Move

4 w

to the left side

4 w^{2} - 3 - 4 w = 0

Write in the standard form

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

4 w^{2} - 4 w - 3 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 4 (- 3) = 8

w_{1, 2} = \frac{- ( - 4 ) \pm 8}{2 \cdot 4}

Separate the solutions

w_{1} = \frac{- ( - 4 ) + 8}{2 \cdot 4}, w_{2} = \frac{- ( - 4 ) - 8}{2 \cdot 4}

w = \frac{- ( - 4 ) + 8}{2 \cdot 4} : \frac{3}{2}

w = \frac{- ( - 4 ) - 8}{2 \cdot 4} : - \frac{1}{2}

The solutions to the quadratic equation are:

w = \frac{3}{2}, w = - \frac{1}{2}

x^{2} + 12 x - 69

3 x^{2} = 12 x^{2} - 144

3 (y + 1)^{2} - 10 (y + 1) + 8 = 0

3 w^{2} + 49 w + 60 = 0

d (x) = 5 x^{2} + 3 x - 4, d (2 x - 3)

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