X+x+2/5x=540

Solution for X+x+2/5x=540 equation:

X+X+2/5X=540

We move all terms to the left:

X+X+2/5X-(540)=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-540=0

We multiply all the terms by the denominator


2X*5X-540*5X+2=0

Wy multiply elements

10X^2-2700X+2=0

a = 10; b = -2700; c = +2;
Δ = b2-4ac
Δ = -27002-4·10·2
Δ = 7289920
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:

$\sqrt{\Delta}=\sqrt{7289920}=\sqrt{64*113905}=\sqrt{64}*\sqrt{113905}=8\sqrt{113905}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2700)-8\sqrt{113905}}{2*10}=\frac{2700-8\sqrt{113905}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2700)+8\sqrt{113905}}{2*10}=\frac{2700+8\sqrt{113905}}{20}
$