1/3x-15=x-5

Solution for 1/3x-15=x-5 equation:

1/3x-15=x-5

We move all terms to the left:

1/3x-15-(x-5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+5-15=0

We multiply all the terms by the denominator


-x*3x+5*3x-15*3x+1=0

Wy multiply elements

-3x^2+15x-45x+1=0

We add all the numbers together, and all the variables

-3x^2-30x+1=0

a = -3; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-3)·1
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{57}}{2*-3}=\frac{30-4\sqrt{57}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{57}}{2*-3}=\frac{30+4\sqrt{57}}{-6}
$