x/(x+27)+(3x+22)+(4x+11)=180

Solution for x/(x+27)+(3x+22)+(4x+11)=180 equation:

x/(x+27)+(3x+22)+(4x+11)=180

We move all terms to the left:

x/(x+27)+(3x+22)+(4x+11)-(180)=0


Domain of the equation: (x+27)!=0

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

x!=-27

x∈R


We get rid of parentheses

x/(x+27)+3x+4x+22+11-180=0

We multiply all the terms by the denominator


x+3x*(x+27)+4x*(x+27)+22*(x+27)+11*(x+27)-180*(x+27)=0

We multiply parentheses

3x^2+4x^2+x+81x+108x+22x+11x-180x+594+297-4860=0

We add all the numbers together, and all the variables

7x^2+43x-3969=0

a = 7; b = 43; c = -3969;
Δ = b2-4ac
Δ = 432-4·7·(-3969)
Δ = 112981
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-\sqrt{112981}}{2*7}=\frac{-43-\sqrt{112981}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{112981}}{2*7}=\frac{-43+\sqrt{112981}}{14}
$