x+35=5/3x

Solution for x+35=5/3x equation:

x+35=5/3x

We move all terms to the left:

x+35-(5/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+5/3x)+35=0

We get rid of parentheses

x-5/3x+35=0

We multiply all the terms by the denominator


x*3x+35*3x-5=0

Wy multiply elements

3x^2+105x-5=0

a = 3; b = 105; c = -5;
Δ = b2-4ac
Δ = 1052-4·3·(-5)
Δ = 11085
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{-(105)-\sqrt{11085}}{2*3}=\frac{-105-\sqrt{11085}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11085}}{2*3}=\frac{-105+\sqrt{11085}}{6}
$