1/3x-15+x+85=180

Solution for 1/3x-15+x+85=180 equation:

1/3x-15+x+85=180

We move all terms to the left:

1/3x-15+x+85-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/3x-110=0

We multiply all the terms by the denominator


x*3x-110*3x+1=0

Wy multiply elements

3x^2-330x+1=0

a = 3; b = -330; c = +1;
Δ = b2-4ac
Δ = -3302-4·3·1
Δ = 108888
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:

$\sqrt{\Delta}=\sqrt{108888}=\sqrt{4*27222}=\sqrt{4}*\sqrt{27222}=2\sqrt{27222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-2\sqrt{27222}}{2*3}=\frac{330-2\sqrt{27222}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+2\sqrt{27222}}{2*3}=\frac{330+2\sqrt{27222}}{6}
$