3/5x+5=x-5

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

3/5x+5=x-5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2+25x+25x+3=0

We add all the numbers together, and all the variables

-5x^2+50x+3=0

a = -5; b = 50; c = +3;
Δ = b2-4ac
Δ = 502-4·(-5)·3
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-16\sqrt{10}}{2*-5}=\frac{-50-16\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+16\sqrt{10}}{2*-5}=\frac{-50+16\sqrt{10}}{-10}
$