((8x-3)/2)^1/2=x^2

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Solution for ((8x-3)/2)^1/2=x^2 equation: 


x in (-oo:+oo)

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

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

((8*x-3)/2)/2-x^2 = 0

(8*x-3)/(2^2)-x^2 = 0

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

2^2*(-x^2)+8*x-3 = 0

8*x-4*x^2-3 = 0

8*x-4*x^2-3 = 0

8*x-4*x^2-3 = 0

DELTA = 8^2-(-4*(-3)*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)-8)/(-4*2) or x = (-16^(1/2)-8)/(-4*2)

x = 1/2 or x = 3/2

(x-1/2)*(x-3/2) = 0

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

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

(x-1/2)*(x-3/2) = 0

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

x in { 1/2, 3/2 }

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