9-x=3/5x

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

9-x=3/5x

We move all terms to the left:

9-x-(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

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

We add all the numbers together, and all the variables

-1x-(+3/5x)+9=0

We get rid of parentheses

-1x-3/5x+9=0

We multiply all the terms by the denominator


-1x*5x+9*5x-3=0

Wy multiply elements

-5x^2+45x-3=0

a = -5; b = 45; c = -3;
Δ = b2-4ac
Δ = 452-4·(-5)·(-3)
Δ = 1965
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{-(45)-\sqrt{1965}}{2*-5}=\frac{-45-\sqrt{1965}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1965}}{2*-5}=\frac{-45+\sqrt{1965}}{-10}
$