x/5x-13=3x+9

Solution for x/5x-13=3x+9 equation:

x/5x-13=3x+9

We move all terms to the left:

x/5x-13-(3x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x/5x-3x-9-13=0

We multiply all the terms by the denominator


x-3x*5x-9*5x-13*5x=0

Wy multiply elements

-15x^2+x-45x-65x=0

We add all the numbers together, and all the variables

-15x^2-109x=0

a = -15; b = -109; c = 0;
Δ = b2-4ac
Δ = -1092-4·(-15)·0
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-109}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+109}{2*-15}=\frac{218}{-30}
=-7+4/15
$