(3/2)(x-4)^2+5=65

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Solution for (3/2)(x-4)^2+5=65 equation: 


x in (-oo:+oo)

(3/2)*(x-4)^2+5 = 65 // - 65

(3/2)*(x-4)^2-65+5 = 0

3/2*(x-4)^2-65+5 = 0

3/2*(x-4)^2-65+5 = 0

3/2*x^2-12*x-41+5 = 0

3/2*x^2-12*x-36 = 0

3/2*x^2-12*x-36 = 0

3*(1/2*x^2-4*x-12) = 0

1/2*x^2-4*x-12 = 0

DELTA = (-4)^2-(-12*1/2*4)

DELTA = 40

DELTA > 0

x = (40^(1/2)+4)/(1/2*2) or x = (4-40^(1/2))/(1/2*2)

x = 2*10^(1/2)+4 or x = 4-2*10^(1/2)

3*(x+2*10^(1/2)-4)*(x-2*10^(1/2)-4) = 0

3*(x+2*10^(1/2)-4)*(x-2*10^(1/2)-4) = 0

( x+2*10^(1/2)-4 )

x+2*10^(1/2)-4 = 0 // - 2*10^(1/2)-4

x = -(2*10^(1/2)-4)

x = 4-(2*10^(1/2))

( x-2*10^(1/2)-4 )

x-2*10^(1/2)-4 = 0 // + -2*10^(1/2)-4

x = -(-2*10^(1/2)-4)

x = 4-(-2*10^(1/2))

x in { 4-(2*10^(1/2)), 4-(-2*10^(1/2)) }

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