13x+10=3/5x

Solution for 13x+10=3/5x equation:

13x+10=3/5x

We move all terms to the left:

13x+10-(3/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

13x-(+3/5x)+10=0

We get rid of parentheses

13x-3/5x+10=0

We multiply all the terms by the denominator


13x*5x+10*5x-3=0

Wy multiply elements

65x^2+50x-3=0

a = 65; b = 50; c = -3;
Δ = b2-4ac
Δ = 502-4·65·(-3)
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-4\sqrt{205}}{2*65}=\frac{-50-4\sqrt{205}}{130}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+4\sqrt{205}}{2*65}=\frac{-50+4\sqrt{205}}{130}
$