-3x+5=5/3x

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

-3x+5=5/3x

We move all terms to the left:

-3x+5-(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

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

We get rid of parentheses

-3x-5/3x+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+15x-5=0

a = -9; b = 15; c = -5;
Δ = b2-4ac
Δ = 152-4·(-9)·(-5)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{5}}{2*-9}=\frac{-15-3\sqrt{5}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{5}}{2*-9}=\frac{-15+3\sqrt{5}}{-18}
$