x+35+1/5x+55+5x-65=180

Solution for x+35+1/5x+55+5x-65=180 equation:

x+35+1/5x+55+5x-65=180

We move all terms to the left:

x+35+1/5x+55+5x-65-(180)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

6x+1/5x-155=0

We multiply all the terms by the denominator


6x*5x-155*5x+1=0

Wy multiply elements

30x^2-775x+1=0

a = 30; b = -775; c = +1;
Δ = b2-4ac
Δ = -7752-4·30·1
Δ = 600505
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{-(-775)-\sqrt{600505}}{2*30}=\frac{775-\sqrt{600505}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-775)+\sqrt{600505}}{2*30}=\frac{775+\sqrt{600505}}{60}
$