6x+(2/3x)=180

Solution for 6x+(2/3x)=180 equation:

6x+(2/3x)=180

We move all terms to the left:

6x+(2/3x)-(180)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x+(+2/3x)-180=0

We get rid of parentheses

6x+2/3x-180=0

We multiply all the terms by the denominator


6x*3x-180*3x+2=0

Wy multiply elements

18x^2-540x+2=0

a = 18; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·18·2
Δ = 291456
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:

$\sqrt{\Delta}=\sqrt{291456}=\sqrt{576*506}=\sqrt{576}*\sqrt{506}=24\sqrt{506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-24\sqrt{506}}{2*18}=\frac{540-24\sqrt{506}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+24\sqrt{506}}{2*18}=\frac{540+24\sqrt{506}}{36}
$