What are the solutions to the equation 3a^2-2x^2=ax ?

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

Find the zeros of 3a^2-2x^2=ax

The zeros of 3a^2-2x^2=ax are x=-(3a)/2 ,x=a

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

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

Solution steps

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

Move

a x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

Simplify

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

5 (x - 3) (x + 5) - 3 (3 x + 19) (x - 5) = 10 (x - 7)

3 n^{2} + 21 n - 510 = 0

432 = (2 x + 18) (2 x + 12)

2 x^{2} = - 10 x

\frac{2}{3} x^{2} + 14 = 20

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