X+5/3x+(2x+20)+(x+15)=180

Solution for X+5/3x+(2x+20)+(x+15)=180 equation:

X+5/3X+(2X+20)+(X+15)=180

We move all terms to the left:

X+5/3X+(2X+20)+(X+15)-(180)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We get rid of parentheses

X+5/3X+2X+X+20+15-180=0

We multiply all the terms by the denominator


X*3X+2X*3X+X*3X+20*3X+15*3X-180*3X+5=0

Wy multiply elements

3X^2+6X^2+3X^2+60X+45X-540X+5=0

We add all the numbers together, and all the variables

12X^2-435X+5=0

a = 12; b = -435; c = +5;
Δ = b2-4ac
Δ = -4352-4·12·5
Δ = 188985
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{-(-435)-\sqrt{188985}}{2*12}=\frac{435-\sqrt{188985}}{24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-435)+\sqrt{188985}}{2*12}=\frac{435+\sqrt{188985}}{24}
$