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

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

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

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2+15x-10x+2=0

We add all the numbers together, and all the variables

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

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