1/3x-15=x1

Solution for 1/3x-15=x1 equation:

1/3x-15=x1

We move all terms to the left:

1/3x-15-(x1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-1x*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}
$