2x-13=6/5x+10

Solution for 2x-13=6/5x+10 equation:

2x-13=6/5x+10

We move all terms to the left:

2x-13-(6/5x+10)=0


Domain of the equation: 5x+10)!=0

x∈R


We get rid of parentheses

2x-6/5x-10-13=0

We multiply all the terms by the denominator


2x*5x-10*5x-13*5x-6=0

Wy multiply elements

10x^2-50x-65x-6=0

We add all the numbers together, and all the variables

10x^2-115x-6=0

a = 10; b = -115; c = -6;
Δ = b2-4ac
Δ = -1152-4·10·(-6)
Δ = 13465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115)-\sqrt{13465}}{2*10}=\frac{115-\sqrt{13465}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115)+\sqrt{13465}}{2*10}=\frac{115+\sqrt{13465}}{20}
$