15=x-1/3x

Solution for 15=x-1/3x equation:

15=x-1/3x

We move all terms to the left:

15-(x-1/3x)=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-1/3x)+15=0

We get rid of parentheses

-x+1/3x+15=0

We multiply all the terms by the denominator


-x*3x+15*3x+1=0

Wy multiply elements

-3x^2+45x+1=0

a = -3; b = 45; c = +1;
Δ = b2-4ac
Δ = 452-4·(-3)·1
Δ = 2037
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{2037}}{2*-3}=\frac{-45-\sqrt{2037}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2037}}{2*-3}=\frac{-45+\sqrt{2037}}{-6}
$