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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply parentheses

2x-1/5x+4-3=0

We multiply all the terms by the denominator


2x*5x+4*5x-3*5x-1=0

Wy multiply elements

10x^2+20x-15x-1=0

We add all the numbers together, and all the variables

10x^2+5x-1=0

a = 10; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·10·(-1)
Δ = 65
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{-(5)-\sqrt{65}}{2*10}=\frac{-5-\sqrt{65}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*10}=\frac{-5+\sqrt{65}}{20}
$