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

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

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

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

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

x = a, x = - 3

Solution steps

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

Subtract

a x + 3 a

from both sides

x^{2} + 3 x - (a x + 3 a) = a x + 3 a - (a x + 3 a)

Simplify

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

Solve with the quadratic formula

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

Simplify

(3 - a)^{2} - 4 \cdot 1 \cdot (- 3 a) : a + 3

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

Separate the solutions

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

x = \frac{- ( 3 - a ) + a + 3}{2 \cdot 1} : a

x = \frac{- ( 3 - a ) - ( a + 3 )}{2 \cdot 1} : - 3

The solutions to the quadratic equation are:

x = a, x = - 3

y, 3 x^{2} + 8 x y + 9 y^{2} = 6

5 a^{2} - 100 = 0

2 x^{2} + 192 = 40 x

X^{2} = 3 X + 4

y^{2} + 2 y + 10 = 0

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