(1-x)/(x+5)=3x+11

Solution for (1-x)/(x+5)=3x+11 equation:

(1-x)/(x+5)=3x+11

We move all terms to the left:

(1-x)/(x+5)-(3x+11)=0


Domain of the equation: (x+5)!=0

We move all terms containing x to the left, all other terms to the right

x!=-5

x∈R


We add all the numbers together, and all the variables

(-1x+1)/(x+5)-(3x+11)=0

We get rid of parentheses

(-1x+1)/(x+5)-3x-11=0

We multiply all the terms by the denominator


(-1x+1)-3x*(x+5)-11*(x+5)=0

We multiply parentheses

-3x^2+(-1x+1)-15x-11x-55=0

We get rid of parentheses

-3x^2-1x-15x-11x+1-55=0

We add all the numbers together, and all the variables

-3x^2-27x-54=0

a = -3; b = -27; c = -54;
Δ = b2-4ac
Δ = -272-4·(-3)·(-54)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9}{2*-3}=\frac{18}{-6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9}{2*-3}=\frac{36}{-6}
=-6
$