(5x-45)+(x+39)+(1/3x+53)=180

Solution for (5x-45)+(x+39)+(1/3x+53)=180 equation:

(5x-45)+(x+39)+(1/3x+53)=180

We move all terms to the left:

(5x-45)+(x+39)+(1/3x+53)-(180)=0


Domain of the equation: 3x+53)!=0

x∈R


We get rid of parentheses

5x+x+1/3x-45+39+53-180=0

We multiply all the terms by the denominator


5x*3x+x*3x-45*3x+39*3x+53*3x-180*3x+1=0

Wy multiply elements

15x^2+3x^2-135x+117x+159x-540x+1=0

We add all the numbers together, and all the variables

18x^2-399x+1=0

a = 18; b = -399; c = +1;
Δ = b2-4ac
Δ = -3992-4·18·1
Δ = 159129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{159129}=\sqrt{9*17681}=\sqrt{9}*\sqrt{17681}=3\sqrt{17681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-399)-3\sqrt{17681}}{2*18}=\frac{399-3\sqrt{17681}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-399)+3\sqrt{17681}}{2*18}=\frac{399+3\sqrt{17681}}{36}
$