What are the solutions to the equation (w^2)/2-w= 3/4 ?

The solutions to the equation (w^2)/2-w= 3/4 are w=(2+sqrt(10))/2 ,w=(2-sqrt(10))/2

Find the zeros of (w^2)/2-w= 3/4

The zeros of (w^2)/2-w= 3/4 are w=(2+sqrt(10))/2 ,w=(2-sqrt(10))/2

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\frac{w ^{2}}{2} - w = \frac{3}{4}

w = \frac{2 + 10}{2}, w = \frac{2 - 10}{2}

Solution steps

\frac{w ^{2}}{2} - w = \frac{3}{4}

Find Least Common Multiplier of

2, 4 : 4

Multiply by LCM=

4

\frac{w ^{2}}{2} \cdot 4 - w \cdot 4 = \frac{3}{4} \cdot 4

Simplify

2 w^{2} - 4 w = 3

Move

3

to the left side

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

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 2 (- 3) = 210

w_{1, 2} = \frac{- ( - 4 ) \pm 2 10}{2 \cdot 2}

Separate the solutions

w_{1} = \frac{- ( - 4 ) + 2 10}{2 \cdot 2}, w_{2} = \frac{- ( - 4 ) - 2 10}{2 \cdot 2}

w = \frac{- ( - 4 ) + 2 10}{2 \cdot 2} : \frac{2 + 10}{2}

w = \frac{- ( - 4 ) - 2 10}{2 \cdot 2} : \frac{2 - 10}{2}

The solutions to the quadratic equation are:

w = \frac{2 + 10}{2}, w = \frac{2 - 10}{2}

b^{2} - 8 b - 20 = 0

4 x^{2} = 64

8 y (2 y + 7)^{4} - 2 y^{3} (2 y + 7)^{9}

21 y^{2} + 11 y - 2

3 n^{2} + 15 n - 72

What are the solutions to the equation (w^2)/2-w= 3/4 ?
The solutions to the equation (w^2)/2-w= 3/4 are w=(2+sqrt(10))/2 ,w=(2-sqrt(10))/2
Find the zeros of (w^2)/2-w= 3/4
The zeros of (w^2)/2-w= 3/4 are w=(2+sqrt(10))/2 ,w=(2-sqrt(10))/2