What are the solutions to the equation a(x-4)=x^2+6 ?

The solutions to the equation a(x-4)=x^2+6 are x=(a+sqrt(a^2-4(6+4a)))/2 ,x=(a-sqrt(a^2-4(6+4a)))/2

Find the zeros of a(x-4)=x^2+6

The zeros of a(x-4)=x^2+6 are x=(a+sqrt(a^2-4(6+4a)))/2 ,x=(a-sqrt(a^2-4(6+4a)))/2

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a (x - 4) = x^{2} + 6

x = \frac{a + a ^{2} - 4 ( 6 + 4 a )}{2}, x = \frac{a - a ^{2} - 4 ( 6 + 4 a )}{2}

Solution steps

a (x - 4) = x^{2} + 6

Expand

a (x - 4) : a x - 4 a

a x - 4 a = x^{2} + 6

Switch sides

x^{2} + 6 = a x - 4 a

Subtract

a x - 4 a

from both sides

x^{2} + 6 - (a x - 4 a) = a x - 4 a - (a x - 4 a)

Simplify

x^{2} - a x + 6 + 4 a = 0

Solve with the quadratic formula

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

Simplify

(- a)^{2} - 4 \cdot 1 \cdot (6 + 4 a) : a^{2} - 4 (6 + 4 a)

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

Separate the solutions

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

x = \frac{- ( - a ) + a ^{2} - 4 ( 6 + 4 a )}{2 \cdot 1} : \frac{a + a ^{2} - 4 ( 6 + 4 a )}{2}

x = \frac{- ( - a ) - a ^{2} - 4 ( 6 + 4 a )}{2 \cdot 1} : \frac{a - a ^{2} - 4 ( 6 + 4 a )}{2}

The solutions to the quadratic equation are:

x = \frac{a + a ^{2} - 4 ( 6 + 4 a )}{2}, x = \frac{a - a ^{2} - 4 ( 6 + 4 a )}{2}

a, a^{2} + b^{2} + c^{2} = 20

3 x^{2} + 2 5 n - 5 = 0

a^{2} x = (a - 1) x^{2} + x

x, k \cdot x^{2} - 10 x + 3 = 0

x^{2} + 10.5 x - 18 = 0

What are the solutions to the equation a(x-4)=x^2+6 ?
The solutions to the equation a(x-4)=x^2+6 are x=(a+sqrt(a^2-4(6+4a)))/2 ,x=(a-sqrt(a^2-4(6+4a)))/2
Find the zeros of a(x-4)=x^2+6
The zeros of a(x-4)=x^2+6 are x=(a+sqrt(a^2-4(6+4a)))/2 ,x=(a-sqrt(a^2-4(6+4a)))/2