x+(2x+1)+(5/2x+3)=180

Solution for x+(2x+1)+(5/2x+3)=180 equation:

x+(2x+1)+(5/2x+3)=180

We move all terms to the left:

x+(2x+1)+(5/2x+3)-(180)=0


Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

x+2x+5/2x+1+3-180=0

We multiply all the terms by the denominator


x*2x+2x*2x+1*2x+3*2x-180*2x+5=0

Wy multiply elements

2x^2+4x^2+2x+6x-360x+5=0

We add all the numbers together, and all the variables

6x^2-352x+5=0

a = 6; b = -352; c = +5;
Δ = b2-4ac
Δ = -3522-4·6·5
Δ = 123784
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:

$\sqrt{\Delta}=\sqrt{123784}=\sqrt{4*30946}=\sqrt{4}*\sqrt{30946}=2\sqrt{30946}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-352)-2\sqrt{30946}}{2*6}=\frac{352-2\sqrt{30946}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-352)+2\sqrt{30946}}{2*6}=\frac{352+2\sqrt{30946}}{12}
$