X+30+x+2/5x+3/5x=180

Solution for X+30+x+2/5x+3/5x=180 equation:

X+30+X+2/5X+3/5X=180

We move all terms to the left:

X+30+X+2/5X+3/5X-(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

2X+2/5X+3/5X-150=0

We multiply all the terms by the denominator


2X*5X-150*5X+2+3=0

We add all the numbers together, and all the variables

2X*5X-150*5X+5=0

Wy multiply elements

10X^2-750X+5=0

a = 10; b = -750; c = +5;
Δ = b2-4ac
Δ = -7502-4·10·5
Δ = 562300
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:

$\sqrt{\Delta}=\sqrt{562300}=\sqrt{100*5623}=\sqrt{100}*\sqrt{5623}=10\sqrt{5623}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-750)-10\sqrt{5623}}{2*10}=\frac{750-10\sqrt{5623}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-750)+10\sqrt{5623}}{2*10}=\frac{750+10\sqrt{5623}}{20}
$