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

The solutions to the equation 3x^2-(3x-2)/4 =(2-x)/3 are x=(5+sqrt(313))/(72),x=(5-sqrt(313))/(72)

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

The zeros of 3x^2-(3x-2)/4 =(2-x)/3 are x=(5+sqrt(313))/(72),x=(5-sqrt(313))/(72)

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

x = \frac{5 + 313}{72}, x = \frac{5 - 313}{72}

Decimal

x = 0.31516 \dots, x = - 0.17627 \dots

Solution steps

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

Find Least Common Multiplier of

4, 3 : 12

Multiply by LCM=

12

3 x^{2} \cdot 12 - \frac{3 x - 2}{4} \cdot 12 = \frac{2 - x}{3} \cdot 12

Simplify

36 x^{2} - 3 (3 x - 2) = 4 (- x + 2)

Expand

36 x^{2} - 3 (3 x - 2) : 36 x^{2} - 9 x + 6

Expand

4 (- x + 2) : - 4 x + 8

36 x^{2} - 9 x + 6 = - 4 x + 8

Move

8

to the left side

36 x^{2} - 9 x - 2 = - 4 x

Move

4 x

to the left side

36 x^{2} - 5 x - 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 36 ( - 2 )}{2 \cdot 36}

(- 5)^{2} - 4 \cdot 36 (- 2) = 313

x_{1, 2} = \frac{- ( - 5 ) \pm 313}{2 \cdot 36}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 313}{2 \cdot 36}, x_{2} = \frac{- ( - 5 ) - 313}{2 \cdot 36}

x = \frac{- ( - 5 ) + 313}{2 \cdot 36} : \frac{5 + 313}{72}

x = \frac{- ( - 5 ) - 313}{2 \cdot 36} : \frac{5 - 313}{72}

The solutions to the quadratic equation are:

x = \frac{5 + 313}{72}, x = \frac{5 - 313}{72}

x, x^{2} + y^{2} = a x

8 x = x^{2} + 15

x^{2} - 40 = 3 x

x^{2} + (x + 14)^{2} = 1156

x^{2} = - x^{2} + 3 x

What are the solutions to the equation 3x^2-(3x-2)/4 =(2-x)/3 ?
The solutions to the equation 3x^2-(3x-2)/4 =(2-x)/3 are x=(5+sqrt(313))/(72),x=(5-sqrt(313))/(72)
Find the zeros of 3x^2-(3x-2)/4 =(2-x)/3
The zeros of 3x^2-(3x-2)/4 =(2-x)/3 are x=(5+sqrt(313))/(72),x=(5-sqrt(313))/(72)