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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)!=0We get rid of parentheses
We move all terms containing x to the left, all other terms to the right
x!=-27
x∈R
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} $
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