(1/2x+3)^2+6=19

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Solution for (1/2x+3)^2+6=19 equation: 


x in (-oo:+oo)

((1/2)*x+3)^2+6 = 19 // - 19

((1/2)*x+3)^2-19+6 = 0

(1/2*x+3)^2-19+6 = 0

(1/2*x+3)^2-19+6 = 0

1/4*x^2+3*x-10+6 = 0

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

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

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

DELTA = 3^2-(-4*1/4*4)

DELTA = 13

DELTA > 0

x = (13^(1/2)-3)/(1/4*2) or x = (-13^(1/2)-3)/(1/4*2)

x = 2*(13^(1/2)-3) or x = -2*(13^(1/2)+3)

(x+2*(13^(1/2)+3))*(x-2*(13^(1/2)-3)) = 0

(x+2*(13^(1/2)+3))*(x-2*(13^(1/2)-3)) = 0

( x+2*(13^(1/2)+3) )

x+2*(13^(1/2)+3) = 0 // - 2*(13^(1/2)+3)

x = -(2*(13^(1/2)+3))

x = -2*(13^(1/2)+3)

( x-2*(13^(1/2)-3) )

x-2*(13^(1/2)-3) = 0 // + -2*(13^(1/2)-3)

x = -(-2*(13^(1/2)-3))

x = 2*(13^(1/2)-3)

x in { -2*(13^(1/2)+3), 2*(13^(1/2)-3) }

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