x+3(-2x+1)/8x+7=8x^2/8x+7

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Solution for x+3(-2x+1)/8x+7=8x^2/8x+7 equation:


x in (-oo:+oo)

x*((3*(1-2*x))/8)+x+7 = x*((8*x^2)/8)+7 // - x*((8*x^2)/8)+7

x*((3*(1-2*x))/8)-(x*((8*x^2)/8))+x-7+7 = 0

x*((3*(1-2*x))/8)-x^3+x-7+7 = 0

(3*x*(1-2*x))/8-x^3+x-7+7 = 0

(3*x*(1-2*x))/8+(8*(-x^3))/8+(8*x)/8+(-7*8)/8+(7*8)/8 = 0

3*x*(1-2*x)+8*(-x^3)+8*x-7*8+7*8 = 0

3*x-8*x^3-6*x^2+8*x-56+56 = 0

11*x-8*x^3-6*x^2-56+56 = 0

11*x-8*x^3-6*x^2 = 0

11*x-8*x^3-6*x^2 = 0

x*(11-8*x^2-6*x) = 0

11-8*x^2-6*x = 0

DELTA = (-6)^2-(-8*4*11)

DELTA = 388

DELTA > 0

x = (388^(1/2)+6)/(-8*2) or x = (6-388^(1/2))/(-8*2)

x = (2*97^(1/2)+6)/(-16) or x = (6-2*97^(1/2))/(-16)

x*(x-((2*97^(1/2)+6)/(-16)))*(x-((6-2*97^(1/2))/(-16))) = 0

(x*(x-((2*97^(1/2)+6)/(-16)))*(x-((6-2*97^(1/2))/(-16))))/8 = 0

(x*(x-((2*97^(1/2)+6)/(-16)))*(x-((6-2*97^(1/2))/(-16))))/8 = 0 // * 8

x*(x-((2*97^(1/2)+6)/(-16)))*(x-((6-2*97^(1/2))/(-16))) = 0

( x-((2*97^(1/2)+6)/(-16)) )

x-((2*97^(1/2)+6)/(-16)) = 0 // + (2*97^(1/2)+6)/(-16)

x = (2*97^(1/2)+6)/(-16)

( x-((6-2*97^(1/2))/(-16)) )

x-((6-2*97^(1/2))/(-16)) = 0 // + (6-2*97^(1/2))/(-16)

x = (6-2*97^(1/2))/(-16)

( x )

x = 0

x in { (2*97^(1/2)+6)/(-16), (6-2*97^(1/2))/(-16), 0 }

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