X+x+x-30+1/2x+5=180

Solution for X+x+x-30+1/2x+5=180 equation:

X+X+X-30+1/2X+5=180

We move all terms to the left:

X+X+X-30+1/2X+5-(180)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

3X+1/2X-205=0

We multiply all the terms by the denominator


3X*2X-205*2X+1=0

Wy multiply elements

6X^2-410X+1=0

a = 6; b = -410; c = +1;
Δ = b2-4ac
Δ = -4102-4·6·1
Δ = 168076
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:

$\sqrt{\Delta}=\sqrt{168076}=\sqrt{4*42019}=\sqrt{4}*\sqrt{42019}=2\sqrt{42019}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-410)-2\sqrt{42019}}{2*6}=\frac{410-2\sqrt{42019}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-410)+2\sqrt{42019}}{2*6}=\frac{410+2\sqrt{42019}}{12}
$