What are the solutions to the equation (2x^2-6)/2 =(15x-9)/6-(3x+14)/8 ?

The solutions to the equation (2x^2-6)/2 =(15x-9)/6-(3x+14)/8 are x=2,x= 1/8

Find the zeros of (2x^2-6)/2 =(15x-9)/6-(3x+14)/8

The zeros of (2x^2-6)/2 =(15x-9)/6-(3x+14)/8 are x=2,x= 1/8

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\frac{2 x ^{2} - 6}{2} = \frac{15 x - 9}{6} - \frac{3 x + 14}{8}

x = 2, x = \frac{1}{8}

Decimal Notation

x = 2, x = 0.125

Solution steps

\frac{2 x ^{2} - 6}{2} = \frac{15 x - 9}{6} - \frac{3 x + 14}{8}

Find Least Common Multiplier of

2, 6, 8 : 24

Multiply by LCM=

24

\frac{2 x ^{2} - 6}{2} \cdot 24 = \frac{15 x - 9}{6} \cdot 24 - \frac{3 x + 14}{8} \cdot 24

Simplify

24 (x^{2} - 3) = 12 (5 x - 3) - 3 (3 x + 14)

Expand

24 (x^{2} - 3) : 24 x^{2} - 72

Expand

12 (5 x - 3) - 3 (3 x + 14) : 51 x - 78

24 x^{2} - 72 = 51 x - 78

Move

78

to the left side

24 x^{2} + 6 = 51 x

Move

51 x

to the left side

24 x^{2} + 6 - 51 x = 0

Write in the standard form

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

24 x^{2} - 51 x + 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 51 ) \pm ( - 51 ) ^{2} - 4 \cdot 24 \cdot 6}{2 \cdot 24}

(- 51)^{2} - 4 \cdot 24 \cdot 6 = 45

x_{1, 2} = \frac{- ( - 51 ) \pm 45}{2 \cdot 24}

Separate the solutions

x_{1} = \frac{- ( - 51 ) + 45}{2 \cdot 24}, x_{2} = \frac{- ( - 51 ) - 45}{2 \cdot 24}

x = \frac{- ( - 51 ) + 45}{2 \cdot 24} : 2

x = \frac{- ( - 51 ) - 45}{2 \cdot 24} : \frac{1}{8}

The solutions to the quadratic equation are:

x = 2, x = \frac{1}{8}

100 = 2 a^{2}

2 x^{2} - 7 x = 0

c, 2 c d - d^{2} = 1 0^{2} + c^{2} - 5^{2}

x^{2} - 765 x + 1 = 0

4 c - 12 = 4 - 4 c + c^{2}

What are the solutions to the equation (2x^2-6)/2 =(15x-9)/6-(3x+14)/8 ?
The solutions to the equation (2x^2-6)/2 =(15x-9)/6-(3x+14)/8 are x=2,x= 1/8
Find the zeros of (2x^2-6)/2 =(15x-9)/6-(3x+14)/8
The zeros of (2x^2-6)/2 =(15x-9)/6-(3x+14)/8 are x=2,x= 1/8