2x-13=-3/5x

Solution for 2x-13=-3/5x equation:

2x-13=-3/5x

We move all terms to the left:

2x-13-(-3/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

2x+3/5x-13=0

We multiply all the terms by the denominator


2x*5x-13*5x+3=0

Wy multiply elements

10x^2-65x+3=0

a = 10; b = -65; c = +3;
Δ = b2-4ac
Δ = -652-4·10·3
Δ = 4105
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{-(-65)-\sqrt{4105}}{2*10}=\frac{65-\sqrt{4105}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4105}}{2*10}=\frac{65+\sqrt{4105}}{20}
$