What are the solutions to the equation roots-6a^2+6b^2+ax+7bx+2x^2 ?

The solutions to the equation roots-6a^2+6b^2+ax+7bx+2x^2 are x=(3(a-b))/2 ,x=-2(a+b)

Find the zeros of roots-6a^2+6b^2+ax+7bx+2x^2

The zeros of roots-6a^2+6b^2+ax+7bx+2x^2 are x=(3(a-b))/2 ,x=-2(a+b)

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roots

- 6 a^{2} + 6 b^{2} + a x + 7 b x + 2 x^{2}

x = \frac{3 ( a - b )}{2}, x = - 2 (a + b)

Solution steps

- 6 a^{2} + 6 b^{2} + a x + 7 b x + 2 x^{2}

The roots are the intercepts with the x-axis

(y = 0)

- 6 a^{2} + 6 b^{2} + a x + 7 b x + 2 x^{2} = 0

Write in the standard form

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

2 x^{2} + (a + 7 b) x - 6 a^{2} + 6 b^{2} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( a + 7 b ) \pm ( a + 7 b ) ^{2} - 4 \cdot 2 ( - 6 a ^{2} + 6 b ^{2} )}{2 \cdot 2}

Simplify

(a + 7 b)^{2} - 4 \cdot 2 (- 6 a^{2} + 6 b^{2}) : 7 a + b

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{3 ( a - b )}{2}, x = - 2 (a + b)

(x - 3)^{2} - 10 = 0

x^{2} - 12 x + c

220900 x^{2} - 4760 x + 16 = 0

z^{2} - 3 z + 4 = 0

y, 3 x^{2} + 2 x y + 5 y^{2} = 24

What are the solutions to the equation roots-6a^2+6b^2+ax+7bx+2x^2 ?
The solutions to the equation roots-6a^2+6b^2+ax+7bx+2x^2 are x=(3(a-b))/2 ,x=-2(a+b)
Find the zeros of roots-6a^2+6b^2+ax+7bx+2x^2
The zeros of roots-6a^2+6b^2+ax+7bx+2x^2 are x=(3(a-b))/2 ,x=-2(a+b)