What are the solutions to the equation 2x^2+3a^2=7ax ?

The solutions to the equation 2x^2+3a^2=7ax are x=3a,x= a/2

Find the zeros of 2x^2+3a^2=7ax

The zeros of 2x^2+3a^2=7ax are x=3a,x= a/2

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2 x^{2} + 3 a^{2} = 7 a x

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

Solution steps

2 x^{2} + 3 a^{2} = 7 a x

Move

7 a x

to the left side

2 x^{2} + 3 a^{2} - 7 a x = 0

Write in the standard form

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

2 x^{2} - 7 a x + 3 a^{2} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 7 a ) \pm ( - 7 a ) ^{2} - 4 \cdot 2 \cdot 3 a ^{2}}{2 \cdot 2}

Simplify

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

x_{1, 2} = \frac{- ( - 7 a ) \pm 5 a}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 7 a ) + 5 a}{2 \cdot 2}, x_{2} = \frac{- ( - 7 a ) - 5 a}{2 \cdot 2}

x = \frac{- ( - 7 a ) + 5 a}{2 \cdot 2} : 3 a

x = \frac{- ( - 7 a ) - 5 a}{2 \cdot 2} : \frac{a}{2}

The solutions to the quadratic equation are:

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

x^{2} - 4 = 0

10 x + 30 = - x^{2}

3 y^{2} + 8 y = 2 y + 9

9 x^{2} - 48 = 0

5 y^{2} - 13 y + 6 = 0

What are the solutions to the equation 2x^2+3a^2=7ax ?
The solutions to the equation 2x^2+3a^2=7ax are x=3a,x= a/2
Find the zeros of 2x^2+3a^2=7ax
The zeros of 2x^2+3a^2=7ax are x=3a,x= a/2