2x=3+1/5x

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

2x=3+1/5x

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-1/5x-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-15x-1=0

a = 10; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·10·(-1)
Δ = 265
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{-(-15)-\sqrt{265}}{2*10}=\frac{15-\sqrt{265}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{265}}{2*10}=\frac{15+\sqrt{265}}{20}
$