What are the solutions to the equation (3x)/4+a/2-(x^2)/(2a)=0 ?

The solutions to the equation (3x)/4+a/2-(x^2)/(2a)=0 are x=-a/2 ,x=2a

Find the zeros of (3x)/4+a/2-(x^2)/(2a)=0

The zeros of (3x)/4+a/2-(x^2)/(2a)=0 are x=-a/2 ,x=2a

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\frac{3 x}{4} + \frac{a}{2} - \frac{x ^{2}}{2 a} = 0

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

Solution steps

\frac{3 x}{4} + \frac{a}{2} - \frac{x ^{2}}{2 a} = 0

Find Least Common Multiplier of

4, 2, 2 a : 4 a

Multiply by LCM=

4 a

\frac{3 x}{4} \cdot 4 a + \frac{a}{2} \cdot 4 a - \frac{x ^{2}}{2 a} \cdot 4 a = 0 \cdot 4 a; a \neq = 0

Simplify

- 2 x^{2} + 3 a x + 2 a^{2} = 0; a \neq = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 a \pm ( 3 a ) ^{2} - 4 ( - 2 ) \cdot 2 a ^{2}}{2 ( - 2 )}

Simplify

(3 a)^{2} - 4 (- 2) \cdot 2 a^{2} : 5 a

x_{1, 2} = \frac{- 3 a \pm 5 a}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 3 a + 5 a}{2 ( - 2 )}, x_{2} = \frac{- 3 a - 5 a}{2 ( - 2 )}

x = \frac{- 3 a + 5 a}{2 ( - 2 )} : - \frac{a}{2}

x = \frac{- 3 a - 5 a}{2 ( - 2 )} : 2 a

The solutions to the quadratic equation are:

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

9 x^{2} + 13 x + 8 = 2 x^{2} + 18 x + 9

w^{2} = 15 w

n^{2} + 1 = 0

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

x, x^{2} y + 2 y = x + 4

What are the solutions to the equation (3x)/4+a/2-(x^2)/(2a)=0 ?
The solutions to the equation (3x)/4+a/2-(x^2)/(2a)=0 are x=-a/2 ,x=2a
Find the zeros of (3x)/4+a/2-(x^2)/(2a)=0
The zeros of (3x)/4+a/2-(x^2)/(2a)=0 are x=-a/2 ,x=2a