-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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1x*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}
$