-5/x1=5/x-3

Solution for -5/x1=5/x-3 equation:

-5/x1=5/x-3

We move all terms to the left:

-5/x1-(5/x-3)=0


Domain of the equation: x1!=0

x^1!=0/

x^1!=√0

x!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

-5/x1-5/x+3=0

We calculate fractions


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

We multiply all the terms by the denominator


(-5x)+(-5x)+3*x^2=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-10x=0

a = 3; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·3·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*3}=\frac{20}{6}
=3+1/3
$