2x-13=6/5x+13

Solution for 2x-13=6/5x+13 equation:

2x-13=6/5x+13

We move all terms to the left:

2x-13-(6/5x+13)=0


Domain of the equation: 5x+13)!=0

x∈R


We get rid of parentheses

2x-6/5x-13-13=0

We multiply all the terms by the denominator


2x*5x-13*5x-13*5x-6=0

Wy multiply elements

10x^2-65x-65x-6=0

We add all the numbers together, and all the variables

10x^2-130x-6=0

a = 10; b = -130; c = -6;
Δ = b2-4ac
Δ = -1302-4·10·(-6)
Δ = 17140
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:

$\sqrt{\Delta}=\sqrt{17140}=\sqrt{4*4285}=\sqrt{4}*\sqrt{4285}=2\sqrt{4285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4285}}{2*10}=\frac{130-2\sqrt{4285}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4285}}{2*10}=\frac{130+2\sqrt{4285}}{20}
$