3/5x=x-1

Solution for 3/5x=x-1 equation:

3/5x=x-1

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-x+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -5; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-5)·3
Δ = 85
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{85}}{2*-5}=\frac{-5-\sqrt{85}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{85}}{2*-5}=\frac{-5+\sqrt{85}}{-10}
$