1+3x=3/5x-2

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

1+3x=3/5x-2

We move all terms to the left:

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


Domain of the equation: 5x-2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2+10x+5x-3=0

We add all the numbers together, and all the variables

15x^2+15x-3=0

a = 15; b = 15; c = -3;
Δ = b2-4ac
Δ = 152-4·15·(-3)
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9\sqrt{5}}{2*15}=\frac{-15-9\sqrt{5}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9\sqrt{5}}{2*15}=\frac{-15+9\sqrt{5}}{30}
$