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

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

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

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

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}
$