What are the solutions to the equation (2x^2+7x-21}{16}-\frac{x^2-3)/4 =x ?

The solutions to the equation (2x^2+7x-21}{16}-\frac{x^2-3)/4 =x are x=-3,x=-3/2

Find the zeros of (2x^2+7x-21}{16}-\frac{x^2-3)/4 =x

The zeros of (2x^2+7x-21}{16}-\frac{x^2-3)/4 =x are x=-3,x=-3/2

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\frac{2 x ^{2} + 7 x - 21}{16} - \frac{x ^{2} - 3}{4} = x

x = - 3, x = - \frac{3}{2}

Decimal Notation

x = - 3, x = - 1.5

Solution steps

\frac{2 x ^{2} + 7 x - 21}{16} - \frac{x ^{2} - 3}{4} = x

Find Least Common Multiplier of

16, 4 : 16

Multiply by LCM=

16

\frac{2 x ^{2} + 7 x - 21}{16} \cdot 16 - \frac{x ^{2} - 3}{4} \cdot 16 = x \cdot 16

Simplify

2 x^{2} + 7 x - 21 - 4 (x^{2} - 3) = 16 x

Expand

2 x^{2} + 7 x - 21 - 4 (x^{2} - 3) : - 2 x^{2} + 7 x - 9

- 2 x^{2} + 7 x - 9 = 16 x

Move

16 x

to the left side

- 2 x^{2} - 9 x - 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 ( - 2 ) ( - 9 )}{2 ( - 2 )}

(- 9)^{2} - 4 (- 2) (- 9) = 3

x_{1, 2} = \frac{- ( - 9 ) \pm 3}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- ( - 9 ) + 3}{2 ( - 2 )}, x_{2} = \frac{- ( - 9 ) - 3}{2 ( - 2 )}

x = \frac{- ( - 9 ) + 3}{2 ( - 2 )} : - 3

x = \frac{- ( - 9 ) - 3}{2 ( - 2 )} : - \frac{3}{2}

The solutions to the quadratic equation are:

x = - 3, x = - \frac{3}{2}

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

- w^{2} + 6 w + 72 = 0

n C^{2} = 15

x^{2} - 12 = 13

x, x^{2} - 3 x y + 5 = 0

What are the solutions to the equation (2x^2+7x-21}{16}-\frac{x^2-3)/4 =x ?
The solutions to the equation (2x^2+7x-21}{16}-\frac{x^2-3)/4 =x are x=-3,x=-3/2
Find the zeros of (2x^2+7x-21}{16}-\frac{x^2-3)/4 =x
The zeros of (2x^2+7x-21}{16}-\frac{x^2-3)/4 =x are x=-3,x=-3/2