What are the solutions to the equation (x^2+1)/2-(2x-3)/4+(x^2)/6 = 59/12 ?

The solutions to the equation (x^2+1)/2-(2x-3)/4+(x^2)/6 = 59/12 are x= 11/4 ,x=-2

Find the zeros of (x^2+1)/2-(2x-3)/4+(x^2)/6 = 59/12

The zeros of (x^2+1)/2-(2x-3)/4+(x^2)/6 = 59/12 are x= 11/4 ,x=-2

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\frac{x ^{2} + 1}{2} - \frac{2 x - 3}{4} + \frac{x ^{2}}{6} = \frac{59}{12}

x = \frac{11}{4}, x = - 2

Decimal Notation

x = 2.75, x = - 2

Solution steps

\frac{x ^{2} + 1}{2} - \frac{2 x - 3}{4} + \frac{x ^{2}}{6} = \frac{59}{12}

Find Least Common Multiplier of

2, 4, 6, 12 : 12

Multiply by LCM=

12

\frac{x ^{2} + 1}{2} \cdot 12 - \frac{2 x - 3}{4} \cdot 12 + \frac{x ^{2}}{6} \cdot 12 = \frac{59}{12} \cdot 12

Simplify

6 (x^{2} + 1) - 3 (2 x - 3) + 2 x^{2} = 59

Expand

6 (x^{2} + 1) - 3 (2 x - 3) + 2 x^{2} : 8 x^{2} - 6 x + 15

8 x^{2} - 6 x + 15 = 59

Move

59

to the left side

8 x^{2} - 6 x - 44 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 8 ( - 44 )}{2 \cdot 8}

(- 6)^{2} - 4 \cdot 8 (- 44) = 38

x_{1, 2} = \frac{- ( - 6 ) \pm 38}{2 \cdot 8}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 38}{2 \cdot 8}, x_{2} = \frac{- ( - 6 ) - 38}{2 \cdot 8}

x = \frac{- ( - 6 ) + 38}{2 \cdot 8} : \frac{11}{4}

x = \frac{- ( - 6 ) - 38}{2 \cdot 8} : - 2

The solutions to the quadratic equation are:

x = \frac{11}{4}, x = - 2

(x + 1)^{2} - (x - 2)^{2} = (x + 3)^{2} + x^{2} - 20

h^{2} - 10 h - 4 = 0

- x^{2} + 320 x - 25.6 = 0

x^{2} + 8 x + 80 = 0

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

What are the solutions to the equation (x^2+1)/2-(2x-3)/4+(x^2)/6 = 59/12 ?
The solutions to the equation (x^2+1)/2-(2x-3)/4+(x^2)/6 = 59/12 are x= 11/4 ,x=-2
Find the zeros of (x^2+1)/2-(2x-3)/4+(x^2)/6 = 59/12
The zeros of (x^2+1)/2-(2x-3)/4+(x^2)/6 = 59/12 are x= 11/4 ,x=-2