What are the solutions to the equation 3/4 ((k^2)/2-2)+k-2= 87/8 ?

The solutions to the equation 3/4 ((k^2)/2-2)+k-2= 87/8 are k=5,k=-23/3

Find the zeros of 3/4 ((k^2)/2-2)+k-2= 87/8

The zeros of 3/4 ((k^2)/2-2)+k-2= 87/8 are k=5,k=-23/3

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\frac{3}{4} (\frac{k ^{2}}{2} - 2) + k - 2 = \frac{87}{8}

k = 5, k = - \frac{23}{3}

Decimal Notation

k = 5, k = - 7.66666 \dots

Solution steps

\frac{3}{4} (\frac{k ^{2}}{2} - 2) + k - 2 = \frac{87}{8}

Find Least Common Multiplier of

4, 8 : 8

Multiply by LCM=

8

\frac{3}{4} (\frac{k ^{2}}{2} - 2) \cdot 8 + k \cdot 8 - 2 \cdot 8 = \frac{87}{8} \cdot 8

Simplify

6 (\frac{k ^{2}}{2} - 2) + 8 k - 16 = 87

Expand

6 (\frac{k ^{2}}{2} - 2) + 8 k - 16 : 3 k^{2} + 8 k - 28

3 k^{2} + 8 k - 28 = 87

Move

87

to the left side

3 k^{2} + 8 k - 115 = 0

Solve with the quadratic formula

k_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 3 ( - 115 )}{2 \cdot 3}

8^{2} - 4 \cdot 3 (- 115) = 38

k_{1, 2} = \frac{- 8 \pm 38}{2 \cdot 3}

Separate the solutions

k_{1} = \frac{- 8 + 38}{2 \cdot 3}, k_{2} = \frac{- 8 - 38}{2 \cdot 3}

k = \frac{- 8 + 38}{2 \cdot 3} : 5

k = \frac{- 8 - 38}{2 \cdot 3} : - \frac{23}{3}

The solutions to the quadratic equation are:

k = 5, k = - \frac{23}{3}

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

\frac{3 x ^{2}}{2} + 8 x + 20 = 0

2 x^{2} - 7 x - 15 = 0

x (x + 15) = 1924

x, x^{2} + y^{2} + 2 x y - 7 x - 6 y + 10 = 0

What are the solutions to the equation 3/4 ((k^2)/2-2)+k-2= 87/8 ?
The solutions to the equation 3/4 ((k^2)/2-2)+k-2= 87/8 are k=5,k=-23/3
Find the zeros of 3/4 ((k^2)/2-2)+k-2= 87/8
The zeros of 3/4 ((k^2)/2-2)+k-2= 87/8 are k=5,k=-23/3