((1/2x-1))^2+((1/2x-1))-90=0

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Solution for ((1/2x-1))^2+((1/2x-1))-90=0 equation:


x in (-oo:+oo)

((1/2)*x-1)^2+(1/2)*x-90-1 = 0

(1/2*x-1)^2+x/2-90-1 = 0

(2*(1/2*x-1)^2)/2+x/2+(-90*2)/2+(-1*2)/2 = 0

2*(1/2*x-1)^2+x-90*2-1*2 = 0

1/2*x^2-x-180-2+2 = 0

1/2*x^2-x-178-2 = 0

1/2*x^2-x-180 = 0

1/2*x^2-x-180 = 0

1/2*x^2-x-180 = 0

DELTA = (-1)^2-(-180*1/2*4)

DELTA = 361

DELTA > 0

x = (361^(1/2)+1)/(1/2*2) or x = (1-361^(1/2))/(1/2*2)

x = 20 or x = -18

(x+18)*(x-20) = 0

((x+18)*(x-20))/2 = 0

((x+18)*(x-20))/2 = 0 // * 2

(x+18)*(x-20) = 0

( x+18 )

x+18 = 0 // - 18

x = -18

( x-20 )

x-20 = 0 // + 20

x = 20

x in { -18, 20 }

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