What are the solutions to the equation 6q^2=8q-3 ?

The solutions to the equation 6q^2=8q-3 are q= 2/3+i(sqrt(2))/6 ,q= 2/3-i(sqrt(2))/6

Find the zeros of 6q^2=8q-3

The zeros of 6q^2=8q-3 are q= 2/3+i(sqrt(2))/6 ,q= 2/3-i(sqrt(2))/6

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6 q^{2} = 8 q - 3

q = \frac{2}{3} + i \frac{2}{6}, q = \frac{2}{3} - i \frac{2}{6}

Solution steps

6 q^{2} = 8 q - 3

Move

3

to the left side

6 q^{2} + 3 = 8 q

Move

8 q

to the left side

6 q^{2} + 3 - 8 q = 0

Write in the standard form

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

6 q^{2} - 8 q + 3 = 0

Solve with the quadratic formula

q_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 6 \cdot 3}{2 \cdot 6}

Simplify

(- 8)^{2} - 4 \cdot 6 \cdot 3 : 22 i

q_{1, 2} = \frac{- ( - 8 ) \pm 2 2 i}{2 \cdot 6}

Separate the solutions

q_{1} = \frac{- ( - 8 ) + 2 2 i}{2 \cdot 6}, q_{2} = \frac{- ( - 8 ) - 2 2 i}{2 \cdot 6}

q = \frac{- ( - 8 ) + 2 2 i}{2 \cdot 6} : \frac{2}{3} + i \frac{2}{6}

q = \frac{- ( - 8 ) - 2 2 i}{2 \cdot 6} : \frac{2}{3} - i \frac{2}{6}

The solutions to the quadratic equation are:

q = \frac{2}{3} + i \frac{2}{6}, q = \frac{2}{3} - i \frac{2}{6}

x - 12 < - 11

(2 x - 3) (x + 7) + (2 x + 3) (x - 7) = - 26

4 \leq x < 10

∣ - 8 + 9 ∣

13 p^{2} - 3 = 4209

What are the solutions to the equation 6q^2=8q-3 ?
The solutions to the equation 6q^2=8q-3 are q= 2/3+i(sqrt(2))/6 ,q= 2/3-i(sqrt(2))/6
Find the zeros of 6q^2=8q-3
The zeros of 6q^2=8q-3 are q= 2/3+i(sqrt(2))/6 ,q= 2/3-i(sqrt(2))/6