2x+3x/5x=1

Solution for 2x+3x/5x=1 equation:

2x+3x/5x=1

We move all terms to the left:

2x+3x/5x-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


2x*5x+3x-1*5x=0

We add all the numbers together, and all the variables

3x+2x*5x-1*5x=0

Wy multiply elements

10x^2+3x-5x=0

We add all the numbers together, and all the variables

10x^2-2x=0

a = 10; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·10·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*10}=\frac{4}{20}
=1/5
$