x+2/3x-15=180

Solution for x+2/3x-15=180 equation:

x+2/3x-15=180

We move all terms to the left:

x+2/3x-15-(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+2/3x-195=0

We multiply all the terms by the denominator


x*3x-195*3x+2=0

Wy multiply elements

3x^2-585x+2=0

a = 3; b = -585; c = +2;
Δ = b2-4ac
Δ = -5852-4·3·2
Δ = 342201
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{-(-585)-\sqrt{342201}}{2*3}=\frac{585-\sqrt{342201}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-585)+\sqrt{342201}}{2*3}=\frac{585+\sqrt{342201}}{6}
$