8/(2x-7)=40(7x-1)

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Solution for 8/(2x-7)=40(7x-1) equation: 


D( x )

2*x-7 = 0

2*x-7 = 0

2*x-7 = 0

2*x-7 = 0 // + 7

2*x = 7 // : 2

x = 7/2

x in (-oo:7/2) U (7/2:+oo)

8/(2*x-7) = 40*(7*x-1) // - 40*(7*x-1)

8/(2*x-7)-(40*(7*x-1)) = 0

8/(2*x-7)-40*(7*x-1) = 0

8/(2*x-7)+(-40*(7*x-1)*(2*x-7))/(2*x-7) = 0

8-40*(7*x-1)*(2*x-7) = 0

2040*x-560*x^2-272 = 0

2040*x-560*x^2-272 = 0

8*(255*x-70*x^2-34) = 0

255*x-70*x^2-34 = 0

DELTA = 255^2-(-70*(-34)*4)

DELTA = 55505

DELTA > 0

x = (55505^(1/2)-255)/(-70*2) or x = (-55505^(1/2)-255)/(-70*2)

x = (55505^(1/2)-255)/(-140) or x = (55505^(1/2)+255)/140

8*(x-((55505^(1/2)-255)/(-140)))*(x-((55505^(1/2)+255)/140)) = 0

(8*(x-((55505^(1/2)-255)/(-140)))*(x-((55505^(1/2)+255)/140)))/(2*x-7) = 0

(8*(x-((55505^(1/2)-255)/(-140)))*(x-((55505^(1/2)+255)/140)))/(2*x-7) = 0 // * 2*x-7

8*(x-((55505^(1/2)-255)/(-140)))*(x-((55505^(1/2)+255)/140)) = 0

( x-((55505^(1/2)+255)/140) )

x-((55505^(1/2)+255)/140) = 0 // + (55505^(1/2)+255)/140

x = (55505^(1/2)+255)/140

( x-((55505^(1/2)-255)/(-140)) )

x-((55505^(1/2)-255)/(-140)) = 0 // + (55505^(1/2)-255)/(-140)

x = (55505^(1/2)-255)/(-140)

x in { (55505^(1/2)+255)/140, (55505^(1/2)-255)/(-140) }

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