5/13x-(x+5)=-5

Solution for 5/13x-(x+5)=-5 equation:

5/13x-(x+5)=-5

We move all terms to the left:

5/13x-(x+5)-(-5)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R


We add all the numbers together, and all the variables

5/13x-(x+5)+5=0

We get rid of parentheses

5/13x-x-5+5=0

We multiply all the terms by the denominator


-x*13x-5*13x+5*13x+5=0

Wy multiply elements

-13x^2-65x+65x+5=0

We add all the numbers together, and all the variables

-13x^2+5=0

a = -13; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-13)·5
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{65}}{2*-13}=\frac{0-2\sqrt{65}}{-26}
=-\frac{2\sqrt{65}}{-26}
=-\frac{\sqrt{65}}{-13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{65}}{2*-13}=\frac{0+2\sqrt{65}}{-26}
=\frac{2\sqrt{65}}{-26}
=\frac{\sqrt{65}}{-13}
$