3/5x=x-2

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

3/5x=x-2

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -5; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-5)·3
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{10}}{2*-5}=\frac{-10-4\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{10}}{2*-5}=\frac{-10+4\sqrt{10}}{-10}
$