(x+12)/(x+5)+1=7x+5

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Solution for (x+12)/(x+5)+1=7x+5 equation: 


D( x )

x+5 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x in (-oo:-5) U (-5:+oo)

(x+12)/(x+5)+1 = 7*x+5 // - 7*x+5

(x+12)/(x+5)-(7*x)-5+1 = 0

(x+12)/(x+5)-7*x-5+1 = 0

(x+12)/(x+5)+(-7*x*(x+5))/(x+5)+(-5*(x+5))/(x+5)+(1*(x+5))/(x+5) = 0

1*(x+5)-7*x*(x+5)-5*(x+5)+x+12 = 0

x-7*x^2-34*x-5*x-25+5+12 = 0

x-7*x^2-39*x-13+5 = 0

-7*x^2-38*x-8 = 0

-7*x^2-38*x-8 = 0

-1*(7*x^2+38*x+8) = 0

7*x^2+38*x+8 = 0

DELTA = 38^2-(4*7*8)

DELTA = 1220

DELTA > 0

x = (1220^(1/2)-38)/(2*7) or x = (-1220^(1/2)-38)/(2*7)

x = (2*305^(1/2)-38)/14 or x = (-2*305^(1/2)-38)/14

-1*(x-((-2*305^(1/2)-38)/14))*(x-((2*305^(1/2)-38)/14)) = 0

(-1*(x-((-2*305^(1/2)-38)/14))*(x-((2*305^(1/2)-38)/14)))/(x+5) = 0

(-1*(x-((-2*305^(1/2)-38)/14))*(x-((2*305^(1/2)-38)/14)))/(x+5) = 0 // * x+5

-1*(x-((-2*305^(1/2)-38)/14))*(x-((2*305^(1/2)-38)/14)) = 0

( x-((-2*305^(1/2)-38)/14) )

x-((-2*305^(1/2)-38)/14) = 0 // + (-2*305^(1/2)-38)/14

x = (-2*305^(1/2)-38)/14

( x-((2*305^(1/2)-38)/14) )

x-((2*305^(1/2)-38)/14) = 0 // + (2*305^(1/2)-38)/14

x = (2*305^(1/2)-38)/14

x in { (-2*305^(1/2)-38)/14, (2*305^(1/2)-38)/14 }

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