9-(6-2x)^2/3=5

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Solution for 9-(6-2x)^2/3=5 equation: 


x in (-oo:+oo)

9-(((6-(2*x))^2)/3) = 5 // - 5

9-(((6-(2*x))^2)/3)-5 = 0

9-(((6-2*x)^2)/3)-5 = 0

(-1*(6-2*x)^2)/3-5+9 = 0

(-1*(6-2*x)^2)/3+(-5*3)/3+(3*9)/3 = 0

3*9-1*(6-2*x)^2-5*3 = 0

24*x-4*x^2-51+27 = 0

24*x-4*x^2-24 = 0

24*x-4*x^2-24 = 0

4*(6*x-x^2-6) = 0

6*x-x^2-6 = 0

DELTA = 6^2-(-6*(-1)*4)

DELTA = 12

DELTA > 0

x = (12^(1/2)-6)/(-1*2) or x = (-12^(1/2)-6)/(-1*2)

x = (2*3^(1/2)-6)/(-2) or x = (-2*3^(1/2)-6)/(-2)

4*(x-((2*3^(1/2)-6)/(-2)))*(x-((-2*3^(1/2)-6)/(-2))) = 0

(4*(x-((2*3^(1/2)-6)/(-2)))*(x-((-2*3^(1/2)-6)/(-2))))/3 = 0

(4*(x-((2*3^(1/2)-6)/(-2)))*(x-((-2*3^(1/2)-6)/(-2))))/3 = 0 // * 3

4*(x-((2*3^(1/2)-6)/(-2)))*(x-((-2*3^(1/2)-6)/(-2))) = 0

( 4 )

4 = 0

x belongs to the empty set

( x-((-2*3^(1/2)-6)/(-2)) )

x-((-2*3^(1/2)-6)/(-2)) = 0 // + (-2*3^(1/2)-6)/(-2)

x = (-2*3^(1/2)-6)/(-2)

( x-((2*3^(1/2)-6)/(-2)) )

x-((2*3^(1/2)-6)/(-2)) = 0 // + (2*3^(1/2)-6)/(-2)

x = (2*3^(1/2)-6)/(-2)

x in { (-2*3^(1/2)-6)/(-2), (2*3^(1/2)-6)/(-2) }

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