(2x-1)^2/3-(1-x)^2/4-3=5/6

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Solution for (2x-1)^2/3-(1-x)^2/4-3=5/6 equation:


x in (-oo:+oo)

((2*x-1)^2)/3-(((1-x)^2)/4)-3 = 5/6 // - 5/6

((2*x-1)^2)/3-(((1-x)^2)/4)-(5/6)-3 = 0

((2*x-1)^2)/3-(((1-x)^2)/4)-5/6-3 = 0

((2*x-1)^2)/3+(-1*(1-x)^2)/4-5/6-3 = 0

(4*6*(2*x-1)^2)/(3*4*6)+(-1*3*6*(1-x)^2)/(3*4*6)+(-5*3*4)/(3*4*6)+(-3*3*4*6)/(3*4*6) = 0

4*6*(2*x-1)^2-1*3*6*(1-x)^2-5*3*4-3*3*4*6 = 0

78*x^2-60*x-216-60+6 = 0

78*x^2-60*x-216-54 = 0

78*x^2-60*x-270 = 0

78*x^2-60*x-270 = 0

6*(13*x^2-10*x-45) = 0

13*x^2-10*x-45 = 0

DELTA = (-10)^2-(-45*4*13)

DELTA = 2440

DELTA > 0

x = (2440^(1/2)+10)/(2*13) or x = (10-2440^(1/2))/(2*13)

x = (2*610^(1/2)+10)/26 or x = (10-2*610^(1/2))/26

6*(x-((10-2*610^(1/2))/26))*(x-((2*610^(1/2)+10)/26)) = 0

(6*(x-((10-2*610^(1/2))/26))*(x-((2*610^(1/2)+10)/26)))/(3*4*6) = 0

(6*(x-((10-2*610^(1/2))/26))*(x-((2*610^(1/2)+10)/26)))/(3*4*6) = 0 // * 3*4*6

6*(x-((10-2*610^(1/2))/26))*(x-((2*610^(1/2)+10)/26)) = 0

( x-((10-2*610^(1/2))/26) )

x-((10-2*610^(1/2))/26) = 0 // + (10-2*610^(1/2))/26

x = (10-2*610^(1/2))/26

( x-((2*610^(1/2)+10)/26) )

x-((2*610^(1/2)+10)/26) = 0 // + (2*610^(1/2)+10)/26

x = (2*610^(1/2)+10)/26

x in { (10-2*610^(1/2))/26, (2*610^(1/2)+10)/26 }

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