x+1/3x+x-8=62

Solution for x+1/3x+x-8=62 equation:

x+1/3x+x-8=62

We move all terms to the left:

x+1/3x+x-8-(62)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/3x-70=0

We multiply all the terms by the denominator


2x*3x-70*3x+1=0

Wy multiply elements

6x^2-210x+1=0

a = 6; b = -210; c = +1;
Δ = b2-4ac
Δ = -2102-4·6·1
Δ = 44076
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:

$\sqrt{\Delta}=\sqrt{44076}=\sqrt{4*11019}=\sqrt{4}*\sqrt{11019}=2\sqrt{11019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11019}}{2*6}=\frac{210-2\sqrt{11019}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11019}}{2*6}=\frac{210+2\sqrt{11019}}{12}
$