3/5x+1=3x-1

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

3/5x+1=3x-1

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-15x^2+5x+5x+3=0

We add all the numbers together, and all the variables

-15x^2+10x+3=0

a = -15; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-15)·3
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{70}}{2*-15}=\frac{-10-2\sqrt{70}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{70}}{2*-15}=\frac{-10+2\sqrt{70}}{-30}
$