x+(2/3x-5)=180

Solution for x+(2/3x-5)=180 equation:

x+(2/3x-5)=180

We move all terms to the left:

x+(2/3x-5)-(180)=0


Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

x+2/3x-5-180=0

We multiply all the terms by the denominator


x*3x-5*3x-180*3x+2=0

Wy multiply elements

3x^2-15x-540x+2=0

We add all the numbers together, and all the variables

3x^2-555x+2=0

a = 3; b = -555; c = +2;
Δ = b2-4ac
Δ = -5552-4·3·2
Δ = 308001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-555)-\sqrt{308001}}{2*3}=\frac{555-\sqrt{308001}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-555)+\sqrt{308001}}{2*3}=\frac{555+\sqrt{308001}}{6}
$