2/5x+x=500

Solution for 2/5x+x=500 equation:

2/5x+x=500

We move all terms to the left:

2/5x+x-(500)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/5x-500=0

We multiply all the terms by the denominator


x*5x-500*5x+2=0

Wy multiply elements

5x^2-2500x+2=0

a = 5; b = -2500; c = +2;
Δ = b2-4ac
Δ = -25002-4·5·2
Δ = 6249960
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:

$\sqrt{\Delta}=\sqrt{6249960}=\sqrt{324*19290}=\sqrt{324}*\sqrt{19290}=18\sqrt{19290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2500)-18\sqrt{19290}}{2*5}=\frac{2500-18\sqrt{19290}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2500)+18\sqrt{19290}}{2*5}=\frac{2500+18\sqrt{19290}}{10}
$